An ultimatum is literally just "a final thing." The menace comes from what happens when it is refused.
The word is Medieval Latin, the neuter form of ultimatus, "last possible, final." Behind it stands the Latin superlative ultimus, "last, final, farthest, most distant, extreme." Etymonline traces ultimus to a root meaning "beyond." The Romans even used the plural ultimata as a noun for what is farthest or most remote: the last, the end.
English adopted ultimatum in 1731. Etymonline defines that first sense as a final demand, proposal or statement of conditions by one party in a negotiation. Merriam-Webster adds the edge the word still carries: a demand whose rejection ends negotiations and usually leads to force or other direct action.
The best-known ultimatum in modern history shows how that works. On the evening of 23 July 1914, Austria-Hungary handed Serbia a list of demands with a 48-hour deadline. Britain's Foreign Secretary, Sir Edward Grey, called it "the most formidable document I have ever seen addressed by one state to another that was independent." Serbia accepted nearly every term but refused to let Austria-Hungary take part in an internal inquiry. Austria-Hungary declared war on 28 July, and Europe followed.
English also had a less dignified use. In the 1820s ultimatum was occasionally slang for the buttocks, presumably a joke on the "last" part of a person. The diplomatic sense outlived it.
The plural is unsettled. Merriam-Webster lists both ultimatums and ultimata, so either is correct.
The same ultimus gave English ultimate, first used in the 1650s in a theological sense, and penultimate, "next to last." The difference is worth keeping. An ultimate thing comes at the end of a series. An ultimatum announces that the series is about to end.