Basic mechanics, you have a portal gun that shoots one blue and one orange portal. Put one on this wall, one on another, and you can walk through either one to get to the other. Use this plus physics to solve puzzles. E3 Demo
Story is you are a test subject being held by one of the best villains in video game history, a sadistic robot named GLaDOS, who gets off on testing (that isn't made up) and delights in the thought of you failing.
Play the first one if you can. Builds the foundation for 2 and is a quick playthough. It was an add on to the Valve Orange Box, which is a great deal in itself if you can find it.