A gaffe is a mistake that embarrasses you in front of others. If you run into a friend out with her grey-haired father, and you blurt out, "Oh, hi, you must be Tara's grandfather!" then you've made a gaffe.
Gaffe rhymes with laugh, and you'll be lucky if that's how people respond to your social blunder. A gaffe seems to occur most often when you literally don't know your audience — you make a joke about the mayor; you didn't know you were talking to his sister. That's definitely a gaffe. And who knew your hosts come from a culture that takes offense if you refuse to try every dish?