Hard to say precisely but "cheddar" seems to have been introduced in the 90s possibly by Bar Area rapper e-40. Some speculate the term comes from selling foodstamps for cash. A possibly related phrase "the big cheese" is much older and may come not from the English word "cheese" but the Urdu word "chiz", meaning "thing." In many hip-hop lyrics, there has been mention of "government cheese", and it wouldn't be a stretch to imagine that this word was modified to mean "money."
So the short of it is, it is not entirely clear how "cheddar" came to mean "money" though you can see some viable possibilities.
Cheddar is commonly used in the context of rhymes citing stacks of-- and alluding to the similar size and shape of commercial cheddar cheese cuts and stacks of US paper currency eg "Ay, ha, ha, better check my swagger How I walk, how I talk, how I stack that cheddar" -T.I. "56 bars" http://www.metrolyrics.com/56-bars-intro-lyrics-ti.html