A tremolo system (more accurately, a Vibrato system) gives the ability for the player to add vibrato to his playing, typically by pushing down on or lifting up on a 'bar' connected to the bridge of the guitar. Pushing down on the bar lowers tension on the strings, thus lowering the pitch of the notes being played. Lifting up on the bar (on some systems) raises the tension and pitch. Subtle variance of pressure on the bar causes very slight fluctuations in pitch, hence the term Vibrato (Tremolo is actually the same note just being played rapidly over and over). More drastic pressure on the bar moves the bridge more and gives more obvious variance in tone, such as the 'Dive Bomb' that was common in 80's guitar playing (ie the end of the Van Halen solo Eruption). Another player who used the Tremolo system a lot was Dime from Pantera. Steve Vai as well.

The system works by counterbalancing string tension with a few springs, which are usually in the back of the guitar, in cavity that has been made for the tremolo system. The Bridge usually rests on a fulcrum point. When the bar is pushed down, the bridge 'tilts' forward, releasing tension on the string while increasing tension on the springs. When the player eases tension on the bar, the spring tension returns the bridge to it's 'zero' point and the strings (theoretically) to their original pitch. I say theoretically because there are a lot of variables involved in this actually happening.

Tremolo systems have existed on electric guitars nearly since the electric guitar became popular (I think the Fender Stratocaster has always had a tremolo, since it's introduction in the late 50's) but didn't come into prominent use until the late 70's/early 80's because heavy use knocked a guitar way out of tune. In the early 80's, Floyd Rose developed and marketed a locking tremolo system where the strings were locked in at the bridge and at the top of the neck by a clamping mechanism. At the bridge, the 'ball end' of the string is cut off and clamped into place on the bridge. The theory behind this is that when the bar is engaged, the string does not move over any surface, eliminating any change in string length (which affects pitch) and eliminates and friction, binding at the nut or tuning head. While not a perfect solution, it improved tuning stability a thousandfold and made it possible for people to get their whammy on.