To regret something is to wish it had never happened. Wish you hadn't reached for that fourth piece of chocolate cake? You regret it.
Regret is often called a useless emotion, because you can only regret what has already taken place. It's too late to change things, so all that's left to do is regret. Regret can also function as a noun, as in the feeling of regret you have when you realize that you should have been nicer to your kid sister and should have not locked her into the dog crate for the afternoon. You often hear people exclaim "No regrets!" when they talk about their life choices, but we're dubious because who doesn't have at least one horrible outfit in their memory that makes them cringe with a feeling of regret?