So bad that nothing can fix it, make it better, or undo it. A remedy is a cure or a fix, so 'irremediable' means 'no cure possible' — not 'very bad', but 'bad and permanent'. You use it for damage, loss, mistakes, situations: an irremediable error, irremediable harm to a friendship. It is a formal, written word — you meet it in books, law, essays, church writing, and speeches, and almost never in normal speech, where people say 'you can't fix it' or 'it's beyond repair'. Two things are worth noticing. First, it is very close to 'irreparable', and in most sentences either one works; 'irreparable' is the commoner one by far, and 'irremediable' has a slightly bookish, sometimes moral flavour — it suits a fault, a condition, a state of the soul, as much as a broken thing. Second, people sometimes use it more loosely to mean 'hopeless, not worth trying with', which the strict meaning does not quite cover, but that use is old and normal in writing.

無法補救的、無可挽回的