Playing a musical instrument makes noise, and sometimes a musician's desire to practice clashes with other people's desire for peace and quiet. For example, a drummer may wish to practice in the basement at night, while a neighbor or someone else in the house wants to sleep. Acoustic foam in the practice area deadens the noise and allows the drummer to play without disturbing anyone.
Another use for acoustic foam is in the recording studio. Producers and engineers use it to deaden the echo in the room where the instrument is being played, or where the amplifier is being recorded. A certain amount of echo can help musicians and producers get the sounds they want to record, but sometimes excess echo is shrill, jarring or just noise that interrupts the performance.
Acoustic design is very important to theaters, lecture halls and anywhere else people assemble to hear someone speak (like a lecturer or actor) or perform music. Acoustic foam prevents sound from bouncing off the walls (room reverberation). Too much room reverberation makes it hard for the audience to hear what the performers are saying or playing. It also makes it hard for the speaker or performer--it's hard to play music and speak when what you just played or said keeps bouncing back at you.
Acoustic foam is handy in any situation where you want to reduce the echo in a room or keep noise from spilling out of the room--firing ranges, ballistics labs, and so on. But it is only as effective as the quality of the installation and the quality of the foam. Denser foams deaden sound better, and higher quality materials last longer.
If you are new to soundproofing, it is best to hire an experienced soundproofer to ensure that the foam you install does the job you want it to do.