When a person correcting someone else's grammar, spelling, or general intelligence makes a grammar or spelling mistake themselves. This does not count if the person has intentionally made the mistake. The phrase comes from "dramatic irony", but is not actually a form of irony.
On an Internet forum:
> > These stupid people are just crybabies who complain when they don't get they're way!
> Your an idiot because you can't spell!
Oh, the grammatic irony....