The basic meaning is to back down on the strength of conviction or integrity about something.
You can compromise in a negotiation by agreeing to terms that were less than you were hoping for. You can compromise in relationships to reach an agreement in an arguement. You can also compromise in your beliefs by letting others pressure you into doing something you believe is not right. So it can be a positive or negative thing, depending on the context.
It can also be used of other kinds of integrity, such as the integrity of the false identity of a spy or undercover police officer, which is said to be 'compromised' when someone discovers them. Or the hull of a ship or any physical structure sometimes can be said to be 'compromised' when it gets damaged.