Just because wifi is on and connected to your wireless network does not mean there is any traffic at all. There would only actually be any active network activity if you had an app or process that needed access to the network. For example, iCloud backups are set to normally occur when the device is plugged in, the screen locked in sleep mode, and an active wifi connection is available. For many people that happens overnight, when they are sleeping and their iPhone is left to charge overnight for the next days use.
There honestly should never be a need to ever turn off wifi, so as raymond says, something must have been actively running over-night. Did you leave any location-based app running in the background? What other background apps do you have enabled? How many items are in your notifications settings? Do you use push email or automatic fetch that might have been actively getting data overnight?