Wi-Fi Assist is just one of the many features that’s come with iOS 9, and it’s enabled by default. That could be very bad news for anyone without an unlimited data plan, because it really adds up to an expensive phone bill if you’re not careful. I’ve got an unlimited data plan so this doesn’t quite apply to me, but for those who don’t, if you see the greyed out Wi-Fi icon, you’ve got Wi-Fi Assist on. I didn’t notice anything since I don’t use Wi-Fi too often, but for those that do, keep a lookout for it. It’s hard to say if the extra costs come from Wi-Fi Assist, but the correlation is worth considering.
If you’re trying to not have this happen to you, it would be in your best interest to simply disable the feature. To disable the feature, go to Settings->Cellular->scroll down to Wi-Fi Assist, and turn it off. (Or search Settings for Wi-Fi Assist.)