What does compromising person mean?

If you compromise with someone, you reach an agreement with them in which you both give up something that you originally wanted. You can also say that two people or groups compromise.

What does too compromising mean?

Something that's compromising makes you vulnerable to being embarrassed or incriminated in some way. If your teacher knows compromising information about you, you might want to ask someone else to write your college recommendation letter. It's common for the adjective compromising to describe the noun situation.