Trumpets have either three or four pistons. These are actuated by the player's fingers and function as a "routing" system for air traveling from the mouthpiece through the instrument. Different combinations of pistons pressed direct the air through different lengths of tubing. Each "path" of tubing alters the pitch of the sound produced when the player blows air through the mouthpiece.
The first valve (located at the bottom) lowers the pitch by two whole tones, the second valve (in the middle) lowers the pitch by one whole tone and a semitone, and the third valve (located at the top) lowers the pitch by one and a half tones.
The valve closest to the mouthpiece is often called the "first valve", the middle valve is called the "second valve" and the valve furthest away from the mouthpiece is called the "third valve".