Margarita,
In acoustic music, a pick-up is an electrical device that attaches to the instrument to convert the sound into electrical impulses. The instrument can then be wired directly to an amplifier to amplify the sound.
For various reasons, performers want "more" sound. The bigger the instrument (generally) the "bigger" the sound. However, practicality limits how big you can make an instrument.
The next step is to use microphones to "pick-up" the sound, convert it to electrical impulses and send it to the sound equipment that amplifies it. There are three major problems with microphones. First, there is "feedback" (that notorious loud whistle that hurts your ears). This results from the microphone picking up sound from speakers or monitors (little speakers facing the performers). Second, there is "bleeding". In a group, the microphone may pick-up sounds of other nearby instruments making it harder to control the blending of instruments. Finally, microphones force the performer to stay nearby the microphone. The further away you get, the less volume you get.
A "pick-up" on the instrument reduces all three of these problems. You won't have feedback unless you do nasty things the way Jimi Hendrix would. Your won't get bleeding if you use a "direct" pickup (that is physically connected to the instrument. You will have more freedom of movement as movement is limited only by the length of the chord connected to the instrument and by your ability to avoid tripping over the wires.
A recent design has been to put small microphones right inside the instrument. They are not technically pickups, but they fit into that category.
Hope this short explanation helps.
Roger in Baltimore