Not all speed runs you see on the Internet are made with the same rules in mind. Here at SDA, we have clear and concise rules to keep in mind when making speed runs for submission to this site. One of those rules bans most forms of emulation.
Emulation means playing a game inside of a program called an emulator. For example, if you have a NES emulator, you can play NES games on a PC, a PSP, or other systems. Thus, you can play the original Super Mario Bros., which has never been released by Nintendo for the PC, on your PC, assuming you can get ahold of the emulator software and a ROM image of the game.
Unfortunately, that last part (getting ahold of a ROM) is usually considered illegal in most parts of the world. The reason for this is obvious: Nintendo won't make any money if you download Super Mario Bros. off of the Internet, versus paying to play the game on the Wii Virtual Console, for example. This is one reason why we don't let you use most emulators to record your speed runs here at SDA (it's usually illegal, and SDA as a whole could get in trouble for it).
Sometimes emulation doesn't work very well, and the game you're emulating will play more slowly or more quickly than it's supposed to. It didn't take long for people to figure out that it's possible to record yourself playing a game at a slower speed than intended, then speed up the resulting video to make it look like you're a better player than you really are. Emulation makes this very easy to do. Of course, if you are competing with someone else who isn't using emulation tools, this is clearly considered cheating, and this is the major reason why we don't let you use emulators to record your speed runs here at SDA.
It turns out that slowing down the game like this and recording a video of a "perfect" playthrough can sometimes be beneficial even to people who have no interest in doing such a thing themselves. There are a couple reasons for this.
First of all, people are fascinated by what it looks like when the human limits of skill and reaction time are removed from speed running. A TAS video, then, is not meant to demonstrate skill at playing a game, but instead to demonstrate what could be possible in the very same game, minus the element of human error.
A second reason TAS can be useful is that sometimes new techniques or gameplay glitches come out during the vigorous testing of a game's engine that occurs when a TAS video of that game is being made. These discoveries can be useful even when making "normal" speed runs that will be accepted to SDA (speed runs not made using emulators). There are many runs on this site that have been made using techniques that first appeared in TAS videos. Some highly successful speed runners even say that watching TAS is essential to understanding the game you are attempting to speed run.
Of course, there are downsides to TAS. Watching such extreme videos can have an emotional effect on people. After all, there is probably no hope of a human ever achieving what is shown in TAS. Some people think that they are so good at a game that nothing could ever beat them, and this is simply not true: every person has limits to their skill, and TAS makes these human limits obvious.
There have also been many occasions when TAS videos have "escaped" and been posted on sites like Youtube and Google Video without an appropriate explanation of what they are. Without seeing a disclaimer, people assume that these videos are made by people playing the game normally, and then they think that legitimate speed runs (as seen here on SDA) are horrible in comparison. If you've been following this document so far, then you understand why speed runs as seen on SDA and TAS videos should never be compared in this way.
You should work hard to educate your friends about the differences between speed runs as seen on SDA and TAS videos as seen elsewhere.
If you are interested in seeing TAS videos, you should check out the largest TAS site, TASvideos (formerly NESvideos). If you are interested in seeing speed runs done by SDA's rules, you can find a list of games right here on SDA.