Gyro is short for gyroscope. For a simple demonstration, hold your dremel tool in your hand while running at high speed. Now, turn your hand different ways. Notice it sort of "resists" movement? Now imagine circuitry that measures this resistance and outputs a signal in proportion to the amount of resistance. Viola!
Here is a decent link on the theory in general. I'm sure you can figure out how it applies to R/C steering...