Used about a bomb, shell, mine, or firework that was meant to explode, did not, and is still sitting there able to go off. That last part is the whole feeling of the word: 'unexploded' is not a calm description, it is a warning. It almost always appears in front of a noun — 'an unexploded bomb', 'unexploded shells', 'unexploded ordnance' — and hardly ever after 'be'. You would say 'they found an unexploded bomb', not 'the bomb was unexploded'. The commonest phrase by far is 'unexploded bomb', usually in news stories about old wartime bombs found on building sites in Europe, where whole streets get emptied while the army takes it away. 'Unexploded ordnance' (often shortened to UXO) is the technical term armies and clearance charities use for all such leftovers — bombs, mines, grenades — and it is worth recognising even though you will never need to say it. English also uses 'unexploded bomb' as a picture for a problem that everyone can see, that nobody has dealt with, and that will go off badly one day: a family secret, a debt, a policy nobody wants to touch. That figurative use is fairly common in journalism and speeches. It is a word you will read more than you will ever say, unless something has gone very wrong.