When you're gaga about something, you feel extremely enthusiastic about it. If your sister is gaga for peanut butter while you can't stand it, you should go through your Halloween candy and give her all your peanut butter cups.
Use the informal gaga for anything you're absolutely wild about, whether you're gaga for kittens or gaga for the beach. It's also used in a somewhat derogatory way to mean "eccentric" or "batty." That quirky old man next door may seem gaga, but once you get to know him you'll realize you've got a lot in common — you're both gaga for chocolate!