Someone unrepentant did something other people think is wrong, and is not sorry about it. The word only makes sense when there is disapproval in the air: people expected an apology, and it did not come. "He remains unrepentant about the comments he made." You can also put it in front of a label to mean someone who happily is that thing and will not stop: an unrepentant smoker, an unrepentant romantic, an unrepentant fan of terrible pop songs. Used that way it is warm and joking — the person is only "guilty" of something small, and the joke is that they refuse to feel bad. That is a very common use and students often miss it. But in news writing it is serious and disapproving: an unrepentant criminal, unrepentant to the end. Two things it does not mean. It does not mean the person did nothing wrong — it says nothing about that, only about their feelings. And it does not mean they are proud, only that they are not sorry; proud is a step further, though unrepentant often hints in that direction. The word comes from religion, where repent means to feel sorry for a sin and turn away from it, but you can use it now with no religious sense at all.