Favorites, represented by a small star icon next to a Tweet, are most commonly used when users like a Tweet and wish to save it for later.
If you've marked a Tweet as a Favorite, you'll see it in two places:
If you're logged in, you can mark any update as a favorite from:
Note: If you mark Tweets as favorites from users with protected profiles, the update will not appear in the favorites tab on your profile page unless the viewer is an approved follower of the update's author.
For example:
To see Tweets marked as favorites:
If you're so over a Tweet and need to remove it as a favorite, just click the star again and it will go hollow, removing the Tweet from your favorites list.
Check out My Favorites Count is Incorrect for more information about this issue.