just wondering…
One important reason is to de-nib - to remove any blemishes in the finish or little bits of fluff or dust that have adhered to the existing coat and are sticking up - this is in order to start the second coat with a good, flat surface. If you try to varnish over such ‘nibs’, rather than just being glossed over, they stick out even more on successive coats.
Another reason is to provide a ‘key’ for the next coat to lock into - this isn’t necessary with all kinds of paint or varnish, but some kinds will tend to delaminate or flake if they’re not keyed between coats.
You will see that (IF you sand between coats) your final finish will have a ‘depth’ to it … especially important if working on a fine-grained wood … the final product will have a quality to it which is hard to describe. Any ‘nibs’ you leave will mar the ultimate effect … think of it like cleaning your sunglasses. Would’nt you rather have a clear view? 
That’s true - whenever you see a really good varnished finish on a piece of furniture (assuming it isn’t French polish or some such), it’s like that because:
-They applied many thin coats (OK, they might have sprayed it)
-They de-nibbed and flattened the surface between coats.
After de-nibbing/flatting, it’s necessary to wipe the piece over with a tack cloth.
If you’re doing finish work, it’s also better to use steel wool in place of sand paper. Better results, much deeper gloss. Just be sure to clean the surface thoroughly after the steel wool or you will end up with millions of little steel wool fuzzies in your finish.
I’ll second the recommendation for steel wool. Use #0000 steel wool (super fine) with a light hand, and be certain that the coat has dried before trying to abrade it down. I found that a shop rag wrapped around a rare earth magnet picked up all the little steel hairs, and that a quick once-over with a clean rag got rid of any excess dust. A tack cloth will probably work just as well.
Some varnishes make a note to not use steel wool.
Right, with any water-base finish, there’s a risk of having rust spots from tiny bits of steel wool that are left behind. Better to use a synthetic abrasive pad in those cases.
Agreeing with what has been said above.
Also, I read an article in a woodworking or furniture magazine some time ago. The article compared different finishes, and one column itemized what each one could adhere to, including other finishes. In the case of polyurethane, the answer was pretty much “nothing other than bare wood”, and that included polyurethane itself. In other words, once polyurethane was applied, it would be difficult to get a second coat of polyurethane to adhere to it very well. Of course, that was not a particularly desirable trait, so preparation work such as sanding/steel wool is actually a requirement if you want to put on a second coat or polyurethane. The other recommendation (if I recall correctly) was to not let the first coat cure too long before applying the next coat. I think that it all has to do with polymerization, but beyond knowing that word I am in over my head.
On preview: Damn, Sal beat me to the steel wool answer. That was my thought as well.
Right. Most polys have a re-coat window along the lines of no sooner than 6 hours after the previous coat and no later than 48 hours. Read the can to know what your specific finish dictates.
If you re-coat too soon, the underlying layer won’t cure properly, possibly resulting in a soft and easily marred finish that will never be right. Wait too long, and the second coat won’t bond and will ultimatley chip off.
When varnishing, the first coat will raise the grain in the wood and this needs to be flattened by abrading. With alkyd varnishes steel wool is better than most other abrasives as it will smooth the surface without scratching and will also ‘key’ sufficiently for a subsequent coat.
The first two or three coats should also be thinned with about 5~10% thinners to allow it to effectively penetrate the grain. The first three coats should be seen as a sealer and not expected to give any indication of the final finish. It is also essential to work very quickly on larger areas to avoid 'tide marks where the edges of the sections overlap - you will never get rid of these tide marks and the job will be spoiled from the start.
It will also bare the grain again so the next coat will also raise the grain where exposed, requiring further abrading and another coat. About 10 to 15 coats with lighter and lighter abrasion and careful cleaning between coats are essential for a first class finish. Generally 16 to 24 hours between coats will allow the material to ‘dry’ sufficiently to receive another coat. Any less (depending on ambient temperature and humidity) and the coating will still be too soft and will be ‘worked up’ by the solvents and thinners in the succeeding coat. Any more and the varnish will be too far into its polymerisation phase to properly bond with the next coat and form a cohesive film.
Where steel wool is counter indicated and sometimes anyway for the final coats, very fine ‘wetordry’ -waterproof carborundum paper - can be substituted very effectively. It is essential that it is used with liberal amounts of water to prevent scratching.
It is also essential to thoroughly wash away any residue which will mar the final finish and allow the surface to dry completely.
It all sounds rather daunting but is well worth it when it is all over, the depth of the gloss is indescribable and wonderful to behold. Lasts for years and years too, far longer than any painted surface. Wood was made to be varnished (or French polished, but that is another saga).
Polyurethane reinforced varnishes are easy to work with - this will be a single pack varnish - but two pack polyurethane or epoxy coatings can be a bit of a nightmare. They will set like concrete a given time after the activator has been added. Nothing will stop it and it can be quite a headache. These materials are generally reserved for marine use or floor coatings for heavily trafficked areas so don’t generally come up under normal domestic situations.
I suspect that we have slightly different standards regarding a first class finish. 
I always thought I was a bit of a perfectionist with 3 or 4 coats.
Everything you ever wanted to know… Almost everything… Well, a lot here about varnish.
I do a few things he suggests. The first coat should be thinned quite a bit as a sealer. He recommends a 1:1 ratio(thinner to varnish). I’ve heard (and use) a 1:2 ratio. It’s funny, the wood seems to drink it up, but if I cut into the piece after it has been varnished, it really didn’t penetrate as far as I would have thought. Then subsequent coats are always thinned before application. It does wonders in avoiding streaks and bubbles, and is worth the extra coats to make up for the thinner.
Depending on the type of finish you don’t necessarily have to sand between coats.
Oil based finishes cure in one of two ways - either by evaporation or reaction. Shellac and lacquer are evaporative finishes; varnish and polyurethane are reactive finishes.
In an evaporative finish, the solids (the actual finish) are dissolved in a solution, and once applied the solution evaporates leaving the solids behind. When you apply another coat over the first coat, the solvent in the second coat dissolves some of the solids in the first coat, so the two coats lock together. So no need to sand.
In reactive finishes the molecules chemically react with each other to form a cross linked bond. Adding a second coat does not dissolve this bond, so the second coat doesn’t fuse with the first as with evaporative finishes. To get the second coat to stick you have to introduce scratches into the first coat so that it can lock in mechanically.
Raising grain should not be a problem with oil based finishes. If you are using a water based finish you’ll want to force the grain to rise by wetting the wood with a sponge, letting it dry, then sanding off **only **the whiskers (the raised grain). As others have mentioned, don’t use steel wool with water based finishes.
I can’t imagine this is right. Even if you add 10% thinner to the varnish, you’ve still got 90% that is the regular varnish/thinner solution. The extra thinner will no doubt penetrate into the grain a bit deeper, but you’re still going to have a good layer of varnish on top. If you’ve got raw wood exposed above the finish you’ve either got a real problem with the prep-work or you are being overly aggressive with the between coat sanding.
I can’t imagine putting 10 - 15 coats on any project. Besides the enormous effort and expense, you are going to end up with a plastic look. 10 - 15 coats is thick!
I don’t think that’s quite right - ‘varnish’ is a catch-all term including any durable, usually transparent and glossy finish - there are polyurethane varnishes (reactive) and evaporative ones - I think in general, we’re talking about the evaporative ones here, because thinning the others is not the usual thing to do.
Ten to fifteen coats does seem excessive, but I have a feeling Myglaren may be talking about a fairly low-solids finish specifically designed to build slowly over many coats.
Ten to fifteen coats of the kind of generic solvent-based ‘varnish’ sold to DIY-ers, even when thinned by 10 or 20 percent, would result in a thick, plastic-like finish - I agree - but ten to fifteen light (perhaps sprayed) coats of thinned, low-build professional varnish might not.
Okay, now I’m a bit confused because I thought that most or all finishes were evaporative. Here’s what I was taught. I have heard of finishes divided into amalgamated and polymer finishes.
Amalgamated finishes include lacquers and shellacs. The solvent evaporates, and the remaining solids form a hard shell. If there is a flaw or damage to the surface, additional solvent can be applied to the surface, re-amalgating the surface which can then be brushed out.
When the solvent in a polymer finish (varnishes) evaporates, the solids lock together with a bond that can’t be broken by the application of additional solvent. The only solution to a damaged polymer surface is to remove and reapply.
With respect to raised grain: Even the finest sanding will leave a very fine fuzz of raised grain. The first coat “freezes” those fibers in place, which are then removed by the first sanding.
With respect to thinning: As mentioned above, the most substantial thinning is only in the first coat to provide a sealer. After that, thinning is mostly to compensate for the inevitable evaporation that takes place during application. A little bit of thinner does wonders to avoid streaking and bubbles.
With respect to multiple coats: I have never applied that many coats, but then again I am easily bored. However, knowing how car enthusiasts will build up coats on their cars for a certain look, it doesn’t surprise me. Consider that a fair amount will be removed after each sanding. It wouldn’t be as thick as you might imagine, especially if thinner was added. And the link that I provided earlier cautions that only glossy varnishes can be applied this way; satin finishes have a flattener that will only obscure the grain with multiple coats.
I’m happy to be corrected if this is incorrect.
Traditionally, they mostly were, but polyurethane varnish cures by reaction with moisture in the air - it may contain solvents, but their primary purpose is to make it mechanically possible to apply via a brush or spray - so their evaporation is pretty much incidental to the process of curing.
There are also a number of two-part finishes - epoxy, polystyrene and polyurethane - that just react to set solid - these may not contain mixed solvents at all and they often set without any significant reduction in volume.
One of the problems in talking about finishes is that the terms used can mean just about anything the manufacturers want them to mean. This is from Bob Flexnor in his book Understanding Wood Finishing:
So I’m confused also, and the more I read up on this the worse it gets. The word “varnish” is essentially meaningless except as Mangetout suggests as a generic term for any transparent finish.