So bad, so cruel, or so wrong that you cannot forgive the person who did it. It is a strong word — you are not saying something was annoying or rude, you are saying it crossed a line and the relationship may not recover. People use it for real betrayals: lying to someone who trusted you, hurting a child, leaving a friend in danger. Note that 'cannot forgive' here is really about feeling, not ability. The speaker is saying 'I refuse to forgive this' or 'nobody should be expected to forgive this'. Because it is so strong, it also gets used lightly and jokingly, and this is very common — 'putting pineapple on pizza is unforgivable', 'he was ten minutes late, unforgivable'. Tone and situation tell you which one is meant; among friends it is usually the joking one. There is also a softer middle use in reviews and complaints: an unforgivable mistake in a company or a piece of work means a mistake that a professional simply should never make. Compare it with 'inexcusable', which is very close in meaning but sounds a little more formal and more about not having a good reason, while 'unforgivable' is about the feeling of the person who was hurt.