I have been playing the game every few days, casually since it launched. At the end of the last season I got bumped a couple of ranks up and earned new card backs. Today I logged in, ranked at 15, it said I earned 10 bonus stars and then it ranked me down to 21, what am I missing here?

Every month the ranks reset. You're given a bonus star for each rank you went up in the previous season.

http://hearthstone.wikia.com/wiki/Ranked_Play

I see! So the bonus stars are applied to rank 25 as a baseline. Thank you, I was just a bit confused there.