An ultimatum is a final demand attached to a threat, like "If you don't do it, I'll never speak to you again." Ultimatums are serious business.
The noun ultimatum has Latin roots meaning "final" and that's still what the word means today. It is the final demand, usually with an implicit or explicit "or else" attached to it. Often, the person on the receiving end of the ultimatum rebels, however, and will say something like, "Don't give me any ultimatums!"