Why are switches grayed out in the iPhones Settings app with iOS 8.3?
Solution 1:
Looks like it's restricted —someone activated parental controls on your device.
Go to Settings > General > Restrictions and scroll down until you see the Cellular data item, you can deactivate it there (given you know the passcode).
On iOS 13, restrictions have been moved under Settings > Screen Time > Content & Privacy Restrictions