Lego Mindstorms is the name of a recent Lego
product family. The key element is the RCX
(a big yellow programmable lego brick).
For those interested in Lego part numbers, the original Mindstorms Robotics Invention System 1.0 (1998-1999) was #9719
It was replaced in 1999 by version 1.5, #9747. The new version has a few (minor) differences in terms of the lego bricks and gears you get with it. The biggest difference was that 1.5 had extra building instructions for three robots.
The Lego Mindstorms sets come with a (rather nasty) GUI programming interface. Programs are written (well, dragged into place) before being uploaded by infrared to the RCX. Fortunately, Dave Baum wrote a rather neat programming language, NQC (Not Quite C) which can be used instead. Even more cool is LegOS, a complete firmware replacement for the RCX, allowing proper C to be written. More recently, LeJOS was released, which is a similar thing, but with Java.
The official Mindstorms website:
Lego Mindstorms Internals
A very nice website listing most technic pieces