Something offbeat is unusual and not what people normally expect, especially in an interesting way. An offbeat film, an offbeat café, an offbeat sense of humour: they stand a little to the side of the main road. The word often carries a small smile; it can be a compliment. It is less wild than off-the-wall. Off-the-wall is “that is crazy.” Offbeat is “that is not the usual pattern, and I rather like it.” The picture behind it is music: the beat is the steady count, and off the beat is the weaker, unexpected place. Jazz lives there. From that, English borrowed the idea for people, clothes, shops, and art. You will still hear the music sense, but in everyday talk the “unusual in a fresh way” sense is the one that shows up most. Informal to neutral. It does not mean wrong, and it does not mean tired. It means the rhythm — of the music, or of ordinary life — is not the one most people keep.