Invective is harsh, abusive language, like, "you dirty rotten scoundrel." I'm sure you can think of harsher and more obscene examples, but we won't get into them here.
Invective comes from the Latin for "abusive." It kind of sounds like a harsh word, actually, with those sharp, dagger-like V's. People usually put a colorful verb or phrase before it. Some examples: "She spewed invective," "She hurled invective," "She burst forth into invective." You can follow it with a phrase like, "picking up her plate and throwing it across the room."