Brownie points is a euphemism for entering into someone's good graces based on doing a favor for them or generally doing right by them. The common usage is you "earn" brownie points.
There are lot of guesses about its etymology, ranging from the Girl Scouts' Brownies (and the helpful elves they were named for) to a magazine distribution method for young boys involving brown vouchers, but given the general pejorative nature of the term, it seems most likely it derived from the term brownnoser and is more similar to "teacher's pet" in usage. The idea of "brown nosing" and a "brownie" evolved sometime around the 1930s, and was most likely spread during World War II by cadets.
Some people still use the phrase as a naif positive, but don't be fooled: those points are brown for one reason only.