If connected to a 1080p display, what is the difference, both technically and in effect?
Someone will offer a much more technical explanation but in a nutshell, if you are upconverting to a higher resolution, the upconverter is interpolating information to fill in the extra resolution. It’s trying to guess what the missing information is. To the average human eye they can do a decent job. With Blu-Ray, there is real information there.
Blu-ray actually has 1080 lines of data in each image, and will therefore give a “real” HD picture. The upconverting DVD player will de-interlace and interpolate the smaller (about 500) lines of data in the DVD signal to give a superior-to-SD image on an HD set, but one that’s clearly not “real” HD visually.
Also, blu-ray players produce pretty much the same image, regardless of brand, whereas upconverting DVD players vary based on the algorithms used.
(And the DVD players are about 1/10 the price).
A 1080p television has 1080 rows of 1920 pixels each. These are actual, physical hardware elements on the TV screen.
If the movie you want to play is organized as 1080 rows of 1920 pixels each, then the television can display the signal exactly. This is what happens with Blu-Ray - the player sends a 1080p signal, and a 1080p TV simply displays it.
Now - if the movie you want to play is smaller (720 rows of 1280 pixels each, for example, or 480 rows of 720 pixels each, as in the case of a DVD), the TV has to massage the signal so that it is still displays on all the pixels. This is called upconverting. Even if you don’t have an “upconverting” DVD player, the TV will do it for you. Unless the source resolution is a multiple of the screen resolution, this will involve some interpolation - 720 does not divide evenly into 1920, for example, so each of the 1920 pixels will be a blend of the nearest pixels in the source.
There are various algorithms for upconverting. Some of them produce better-looking output than others. For various reasons, it is easier for a DVD player to perform high-quality upconverting than a TV.
However - upconverting cannot add detail that isn’t there in the original source material. All it can do is make the resolution difference between the source material and screen less noticeable. A Blu-Ray picture has approximately 6x more detail than a DVD, regardless of what algorithm you use.
http://avalys.net/hd has a comparison of DVD resolution (on the left) with Blu-Ray (on the right).
Oh, and one downside (other than price) of Blu-Ray - they need to be upgraded frequently at the firmware level in order to keep playing new disks because of copy protection and feature upgrade schemes. Some companies are good about releasing the upgrades quickly, some not, and some players aren’t upgradeable at all (and won’t say so on the packaging). You won’t know you need an upgrade until a disk gives you a “sorry, not on this player” message.
In my opinion (which I feel free to give now that the OP’s been answered three times), this is a fiasco on the order of the +R/-R/-RAM nonsense with CD’s and DVDs. Until they get it sorted out (or if you can get a BR player at a price you consider disposable), I’d wait it out, or be very careful in your research before buying.
Thank you all - great answers - even one to a question I didn’t know to ask…
This place is still pretty damn awesome.
This is an excellent summary and example. One thing to note though, is that depending on the size of the screen and how far away you sit from it, you may not notice the difference. Many people who say they don’t appreciate the improvement from an HD source are looking at it on a screen size of, say, a 42" diagonal, but are looking at it from 8 or even 10 feet away (as they just dropped the new HDTV in the same place as their old regular TV with the same viewing distance), at which distance the blockiness of the lower-res picture being upconverted isn’t really visible, and the difference between 10280i/p and 720p resolution, and possibly even standard TV resolution, is pretty much nil.
Going for 1080p resolution is only really worth it (IMHO) if you’re going to be sitting close to the image (1.5x the screen width away) to appreciate the depth of clarity in the big picture. Here’s a screen size/distance calculator to help figure out the best bang for the buck. For full HDTV resolution (1080) and a 42" diagonal screen size, once you’re sitting farther away than 5.5 feet from the screen you will not see the full benefit – either sit closer, get a bigger screen or settle for 720p and save some cash. (Sitting 5.5 feet away from an HD image at 42" diagonal is equivalent to sitting 14.6 feet away for a standard-def TV image, which illustrates how much better the image quality is, and also how you need to sit closer or get a bigger picture to take advantage of that!)
Does free qualify? 
(Thank-you, Sony and Best Buy!)
Yes, I could probably manage to save up for free. What deal are you seeing?
A Sony 32" 1080 HDTV coupled with their Blu-Ray player. $999 for the TV, $999 for the TV and the player. Both of which sit in my upstairs loft, where the TV will be used alternatively for gaming (not interested in the PS3, tyvm, which plays Blu-Ray discs) and some movie watching.
Now, alternatively, the Sony 40" HDTV is being offered for $1399 with the Sony PS3. But that TV alone is only $1199, so you are getting the PS3 for about half-price that way. I didn’t want something that big, nor did I want to spend over $1000. 