Someone incorrigible seems to be beyond correcting or improving. When you talk about an incorrigible drunk, you're saying they're never going to stop drinking.
Even though incorrigible implies a person is kind of hopeless, it's often used as a light-hearted word. When we describe someone as an incorrigible flirt or as an incorrigible gossip, we mean that this is just the way they are, and it would be foolish to try and change them. If someone is just being obnoxious as usual, you could say "You're incorrigible!"
