There a few things that it could be. However, to know more, what kind of phone is it, and who is your carrier?
In regard to the signal strength, that only tells you how good your phone is allowing it. It will not, however, tell you if you actually are connecting to WiFi or if you have data available/left on your plan. So do you have that on your plan? And are you near any WiFi connections? Well I should say, either open WiFi connections or ones you have the password for?