An example of something similar to a TAS is a Piano Roll, look at this video: http://www.youtube.com/watch?v=5395Y0hwJGU
With a Piano Roll you can get a piano to play any notes, even faster or more complex than what a human would be able to play. You can take all the time in the world to prepare your Piano Roll in the way you want it to be, and if there is a mistake, you can re-record it to play in the correct way.
Likewise, a TAS is a list of button presses, ideally (or really, see Nesbot and Droid64) fed to a joypad, to play a game as perfectly as possible, even doing things a human can't do. There are several ways to create a TAS, with many tools you can use (hence the name). You can slow down the game and play a single frame (to make it simple, 1/60th of second in America, and 1/50th of second in Europe), you can go back and fix your mistakes, you can find out that the "random" ites are not really random and manage to get the best items all the times, and so on. Nobody prevents you from using all the techniques in the world while you create that list of button presses
. Once it is ready, that input should always replay in the same way (still like the Piano Roll); if it desyncs, then something went wrong.
Many TAS-related concepts can find examples in simple words in the real world. For example, you might read of a "frame rule" sometimes, e.g. "I can beat that level 10 frames faster but there is a 20 frames rule so it's pointless". Imagine you're on the street, running towards the station because you have to catch a train. Of course you try to run as fast as you can, but... there is a traffic light right next to the station. If you arrive there while the traffic light is red, all your running was wasted because you have to wait for the green. This is a frame rule. If this happens in a TAS, the "runner" can either slow down (but it would look unprofessional and not entertaining) or do something unexpected to keep the viewer's interest, such as collect all the coins, kill all the enemies, run backwards, dance, whatever. As long as you arrive at the traffic light in time for the green.
My English is bad but I hope this is clear.
Either way, welcome to the forum!