Photo Stream is a special picture folder on your iOS devices and iPhoto on your Mac that automatically captures all of your recent photos. This folder is kept in sync between all of your devices. It’s quite a cool feature, but unless you need to access your photos immediately on other devices I recommend turning it off.
Why turn it off? Every photo you take is duplicated, meaning every photo you take consumes twice the amount of storage on your iPhone. It also means that when it comes time to sort out and delete unwanted photos you have to delete them from two locations.
To turn off Photo Stream go to the Settings app > iCloud > Photo Stream. You can turn off your regular Photo Stream while still using Shared Photo Streams if you want to share specific photos. Photo Stream can also be disabled in iPhoto Preferences on your Mac.