An indignity is something embarrassing. An indignity is usually something that happens to us rather than something we do ourselves.
As you might guess from that negative prefix in-, an indignity is a word that takes dignity (or self-esteem) away. If you find a fly in your soup, that's an indignity — not to mention protein. If you're making a speech and you realize your fly is open, that's a major indignity. Many people find waiting in line a long time to be an indignity. When you say "This is an indignity!" you're really saying, "I'm better than this, and I shouldn't have to deal with it." Needless to say, life is full of indignities.