Photo Stream is an Apple cloud syncing feature of iOS that automatically uploads your latest 1000 photos to iCloud, and shares them across all your iOS devices, and with specified friends and family. While the feature can be cool, it can also be creepy, knowing that no matter what you photograph, it is also being stored somewhere out there, in the cloud.
The first way to completely disable Photo Stream is to not have an iCloud account. No iCloud, no Photo Stream. The second way to turn it off is to go to Settings, and switch My Photo Stream and Shared Photo Stream from “On” to “Off.” Remember, to completely disable Photo Stream, you will need to modify the settings on each of your iOS devices, such as iPhones, iPads, and Macs.
How to Disable Photo Stream