In most guns after the last round is fired bolt stays back so weapon can be quickly reloaded without the need of pulling the bolt back.
How does this mechanism work?
There’s a catch, like on a door latch, that is held down by the bullets. Once the last round is fired it pops up and engages the bolt.
chacoguy is sort of correct. The plate at the bottom of the magazine, upon which the last round lays, is called the follower. You’ll notice that on most magazines there is a cutout on the magazine body (usually at the front like this Sig Sauer magazine) such that the follower engages the slide/bolt lock (which rides inside the frame) and locks the slide in place. If the slide or bolt is cycled on a loaded magazine or without a magazine, the slide/bolt lock is not engaged and the action cycles normally.
Note that some people refer to the lever on the side which is connected to the slide lock as the “slide release”, but in reality the slide should be released by pulling back on the slide with a load magazine/no magazine, or holding down the slide lock while cycling the action. Depressing the slide lock lever to release the slide puts undue stress and wear on the slide lock which will eventually cause it to fail to lock back.
Stranger
This is a Sig P238 slide lock.
http://i210.photobucket.com/albums/bb256/GaryM_photo/20140718_222132.jpg
The part with the poorly drawn arrow is pushed up by the magazine follower as stated by Stranger after the last round is fired and ejected. This allows the part just in front to catch the slide as it tries to move forward powered by the recoil spring. The slide stop is normally held down by a light spring.
Just because I enjoy being a pedantic little prick, the OP asked why the bolt stays back and both of you gave examples of why the slide stays back.
Yes, I know it works the same way, but I am a gun nut. Clearly, the OP is not.
I’d tell a laymen that the slide on an autoloading pistol and the bolt, or bolt and bolt carrier group, on an autoloading rifle or shotgun serve the same purpose, so for this discussion it’s the same.
And in weapons firing from an open bolt the sear holds the bolt back.
And in some firearms, you cannot slide the “thingy” forward again without depressing the catch slightly. Be careful! You don’t want Garand/M1 thumb! (w/ pictures)
On some semi or fully automatic rifles, the bolt stays open. On some it does not(?). On some it is open all the time except in the middle of a shot.
Let’s not even mention revolvers. Nothing to see here…
My training rifle was the M1. Our training Sgt. must have been a good one because our whole barracks never had one finger or thumb hurt…
Or we were special snowflakes & didn’t know it. 
We’re all special, just in different ways!
Weapons which fire from an open bolt are the playthings of Murphy.
Stranger
A slide stop on a Colt 1911 costs about $25 (or half that on eBay). A bolt catch for an AR-15 cost about $7. The slide stop on the Colt is removed when the pistol is cleaned, so replacing it is a non-issue. The bolt catch on the AR-15 is held in place by a roll pin and is not normally removed; but it’s also easily replaced. I shouldn’t worry about wearing them out. If they wear out, just pop in new ones.
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Why you wanna tease the rubes like that? Revolvers have bolts and hands and all manner of partz.
Having the slide stop fail in a combat situation is not something you want to deal with. Although it won’t stop the weapon from functioning, it will not give the proper indication that the magazine is empty, and under the stress of combat the shooter may not perceive that the weapon is no longer firing. In any case, manipulating the slide stop generally means changing the grip on the shooting hand to reach the stop, which is also undesired (with a pistol, at least; with rifles you generally have to reload using the shooting hand anyway). In general, it is an unnecessary and inefficient way of releasing the slide or bolt versus just pulling back and releasing the slide or charging handle.
Stranger
QFT.
It must be said that this is a HOTLY debated topic in the shooting community. Right up there with 9mm vs. .45 and what kind of lube you should use on your guns. And it’s not just “people” who refer to it as a slide release, some manufacturers themselves actually use that terminology. For example, companies like Glock install extended slide stops right from the factory on their “competition” models like the 34 and 35 where the vast majority of shooters use the slide stop to drop the slide. Surely, they wouldn’t be offering these things if they didn’t intend on people using them to drop the slide.
Anecdote warning: I’ve been involved in the competition shooting community for years and have encountered many guns well north of 100,000 rounds fired. I’ve yet to encounter someone that wore out a slide or slide stop/catch/release/whatever from using it to drop the slide. Certainly not to the point where it no longer function.
With regard with bolts you find on rifles like the AR, pulling back to charging handle has largely fallen out of favor over just using the bolt catch. I’m not aware of any prominent instructor or competition shooter that advocates it.
Unnecessary is a matter of debate. Inefficient? How, exactly is it inefficient? It certainly isn’t any *slower *than using the slingshot method you advocate; try running both approaches on a timer. Being able to release the slide immediately after magazine insertion and while transitioning directly to a firing grip has far more economy of motion than reaching up to pull back on the slide. One can debate the various merits of using the same motion to drop the slide as you use to clear malfunctions, being able to use the same motion across different guns with wildly varying slide stop positions, etc. Then again, one could also make an argument about all the shooter induced malfunctions that occur from people inadvertently riding the slide or bolt forward with their hand, but these are all separate matters.
My point here, is that there are varying schools of thought on this topic, and since many people on this message board aren’t familiar with firearms, it bears mentioning.
Air Force here, we’re taught to use the slide release/bolt release to send the slide/bolt forward on the Beretta 92 or the AR-15 (well, M9 and M16/M4, but you know what I mean). I’m not sure what would happen if I inserted a fresh magazine and started tugging on the tail end of the slide, other than that I’d get my last warning from the rangemaster for fucking around instead of following instructions.
As for wear and tear, I guess that’s why the military has professional armorers to maintain the weapons beyond your routine cleaning. Private gun owners of course don’t have that benefit and any specialized work is going to be out of pocket for them.
Well, yeah, the military wants them to wear out to have an excuse to buy new toys. 
Do we have any empirical evidence that using the slide release (can be) bad? Or even if means that it might wear faster but the change is minuscule so it doesn’t matter much? It does sort of remind me of the perennial debate over whether it is okay to leave magazines loaded indefinitely (last I checked, it’s fine).
I just learned that the SCAR changes from closed to open bolt as it heats up. Interesting.