No internet
When I leave home I have no internet on my iPhone. Why? I do have it before.
iPhone 4s, iOS 9
When you leave Home, use Public Wi-Fi, sSee this Apple article: Use captive Wi-Fi networks on your iPhone, iPad or iPod touch -> Use captive Wi-Fi networks on your iPhone or iPad – Apple Support (UK)
Nowadays, Public Wi-Fi is offered for free, in big cities, shopping centers, in Public Transport (bus & train), airport, restaurants, hotels and others.
That depends on where you live.
If at the moment you are away from home and there is no Public Wi-Fi, you have to use Mobile Data, for sure go to -> Settings -> Mobile network -> Mobile Data -> ON.