Embarrassment is the feeling you have when you are embarrassed.

An embarrassment is an action, event, or situation which causes problems for a politician, political party, government, or other public group.

If you refer to a person as an embarrassment, you mean that you disapprove of them but cannot avoid your connection with them.

If you say that someone has an embarrassment of riches, you mean that they have so many good things that these things are a problem.