The adverb of unmistakable: in a way that nobody could get wrong. You use it in front of an adjective or a noun-ish description to say 'this is so clearly true that there is no arguing': 'unmistakably Taiwanese', 'unmistakably angry', 'unmistakably his handwriting'. Think of it as a stronger, more elegant 'very clearly' or 'without any doubt'. One useful thing to notice: it usually attaches to WHAT something is, not to how well something is done. So we say 'the tune is unmistakably Japanese' — the tune could not be from anywhere else — rather than 'she sang unmistakably'. It also often carries a small note of recognition, as if you are pointing at something and saying 'ah, that one, I know it'. Speakers use it in reviews, in descriptions, and when identifying people or styles. It is a bit formal, so in casual talk your friends would probably just say 'definitely' or 'you can totally tell'.