WiFi assist is one of the new features in iOS 9. For most users it’s great but for some it may cause headaches depending on their specific data plans or application requirements.
Here’s some more information on exactly what Wi-Fi Assist is, and why you may actually want to turn it off on your iPhone.
Apple’s support article: About WiFi assist: https://support.apple.com/en-us/HT205296
Video / How to disable Wi-Fi assist on Apple iOS 9 devices