A pick up is the name for a transducer which will convert vibrations into electrical signals for Amplification. Pick ups are used on Instruments (as opposed to a Microphone) and will specifically respond to the instrument rather than any background noise, other instruments or voices.
Instruments may use pickups as the sole means of generating the sound (ultimately, through the Amplifier and Loudpeaker) and these are purely Electric Instruments such as the Electric Guitar. Increasingly, Acoustic Instruments are fitted with Pick Ups to make them Semi-Acoustic: that is they will sound like an acoustic instrument but can be amplified if the need arises.
Portable Pick Ups are available to clip onto Acoustic Instruments to temporarily convert them to Electrically Amplified.
For Electric Instruments and Semi-Acoustic, the Magnetic Pick Up is the norm. This is similar in construction to a dynamic microphone with a magnet and a coil of wire except that in the Pick Up they remain stationary and the metal strings interrupt the magnet field and induce a signal in the coil of wire. They are mounted forward of the bridge on the body of the instrument and under the strings.
For some Semi-Acoustic and the majority of Acoustic instrument Pick Ups, the Piezoelectric type is used. These are mounted under or inside the bridge.