I am thinking a cellphone, yet i am not sure because there are a lot of things that can be turned on the size of you palm.
Cellphone
MP3 player
TV Remote Control
Your Finger/Thumb (finger can fit inside a palm, can be hard because of bone, and most people use a finger/thumb to operate a button)
Man, the things i love to hate about riddles........they are too vague!! LOL