On a string instrument, the bridge is a component that juts out from the main body and supports the strings. It holds the strings away from the body of the instrument (so they are free to vibrate) and transmits the vibrations to the body. On most string instruments, the bridge is made of a flat piece of wood, and is often intricately carved. Use this tag for questions about bridges on string instruments.
Acoustic guitars usually have flat bridges, with a saddle that sits atop the bridge, in contact with the strings. Use this tag for questions about bridges and saddles on guitars.
Electric guitars usually have metal bridges. They often have some freedom of movement to allow tremolo or vibrato effects, including systems of springs and/or a tremolo arm. Use this tag for questions about any part of such a bridge.
Bridge is also a composition term, especially common in pop music: a phrase that carries the music from one phrase (such as the chorus) to another (such as the next verse). Often the phrase after the bridge is a reprise of the main motif of the piece, and the bridge itself adds some contrast to this. Don't use this tag for that, or things will get very confusing.