It's interesting to me because Facebook just made the news recently for saying they'd try to come up with something akin to dislike because the "like" is too positive a sentiment for many situations (death of a relative, bad day at work, whatever). In the wake of that, Twitter didn't say "well the favorite is already neutral of emotions, and is more akin to showing support for the thing, positive or negative". Instead, they said "oooh, we want the problem Facebook is facing".
When I first joined twitter I assumed that "favorites" were bookmarks and didn't realize that twitter notified users when you favorited a tweet.
A lot of people use it as a way to get your attention without retweeting the post to their feed. I've started getting an increase in what seems to be automated favoriting (now liking), which is so incredibly annoying that I have to end up muting those users.