To decompress is either to reduce physical pressure on something or to unwind and relax after a long, hard day. You might need to decompress after a four-hour study session with your math tutor.
When you compress something, you squeeze or flatten it, the way you'd compress an air mattress before rolling it up. If you decrease or let up that pressure, you decompress the air mattress. It's much more common to use this verb to mean "relax," to loosen a completely different kind of pressure. You may decompress after school by watching TV or taking your dog for a walk.