Riddance is the act of getting rid of something. People say "Good riddance!" when they're happy someone or something is gone.
When you're rid of something, it's gone. You're rid of a cold when it's over. Similarly, riddance is the action of getting rid of something. The police are dedicated to the riddance of crime. Librarians want riddance of noise so people can read. If you have bugs where you live, you're going to be interested in their riddance: they will have to be exterminated. Good riddance!