What can I do with an unlocked iphone?

I haven't unlocked it because I don't know that any company can legally activate it. It is from Verizon. It was given to us by my mom. I believe it is an iphone4.

Added (1). what cell company can I activate it through after the unlock?

Anything you want

Unlocks concern GSM phones for the record. Verizon is a CDMA network. If you have an unlocked phone you can use it on any GSM carrier in the world, vs being locked where you can only use it on one, usually the one it was bought from e.g. AT&T.

In the case of a CDMA phone you'd have to try to flash the software & hope another CDMA carrier (like Sprint) would activate it on their network.