Kaç tane? means “how many?”. It’s used for countable nouns.
Tane means “a single thing, item, piece ” as in bir tane domates (a tomato). It is not always necessary to use tane, but it’s commonly used (even overused) by Turkish speakers, not only for things but also (very surprisingly) for people as in bir tane kadın (a woman), bir tane adam (a man). It’s usually left untranslated.