It came out of research at Harvard (by the authors of Getting to Yes) and is related to game theory. So it's academic (and therefore jargony) but is probably also intended to be more precise than alternatives or options.
That said, for day to day use, understand your alternatives if the parties can't come to an agreement works perfectly well.
IMHO there's a difference - alternatives and options are the things that you consider and discuss might offer to the other party within a negotiation, they are a part of it.
BATNA, on the other hand, is outside of that negotiation, it is the thing that you'll actually do if the negotiation fails. This will not always will match your statements during the negotiation about what your options are, it's something purely in your mind to compare with the actual alternatives being negotiated and something which, unlike these alternatives, does not require a negotiated consent of the other party.
Even just knowing the concept gets you halfway there, assuming you have any other options at all. It's a term everybody should know. BATNA BATNA BATNA!