TASing is the method of using various tools (excluding cheating devices like game genies) and glitches to beat a game in the fastest time possible. Some TAS videos are simple, others are outrageous.
I love these kinds of videos, because it's kind of like how a superhero would play video games.
And here's a site specifically for TAS runs and videos: tasvideos.org
Here's a really crazy run of Tails in Sonic 1: http://tasvideos.org/2514M.html