It's like a magic volume control that turns itself down when the sound gets louder than a certain point. Exactly how much it turns the volume down, how fast it responds and how quickly it turns the volume up again after the sound gets quieter again are adjustable and require skill and experience to make the effects of compression as inaudible as possible while still having it do something useful.

And the reasons for using it include:
- easier to keep the sounds balanced when mixing
- compensating for vocalists with bad mic technique (especially in live sound)
- adding more sustain to instruments that naturally decay like plucked   stringed instruments
- by reducing the peaks you can afford to raise the overall level so everything's louder (this is universally overdone on the radio)

Anahata