Why my iPhone uses celluar data instead of WiFi ?

I put money on my phone count, usually that would be enough for a 3-4 weeks, but i entered internet during a week and recently spotted all the money had gone. I turned all strings off in Settings>General>Celluar except celluar data. I mean off 3g, data roaming and all below. Only celluar data stayed on. I tried to use the internet with my WiFi, but it tells me there is no internet connection, but my WiFi is turned on. Help me please solve the problem, why my phone uses celluar internet instead of WiFi ?