The iPhone's cellular data network is the component of its carrier-based service that enables its "always-on" mobile Internet. If the error message "You are not subscribed to a cellular data service" flashes across the screen, it may or may not reflect a permanent problem with the iPhone's cellular data network.
If the error message "You are not subscribed to a cellular data network" appears on your screen, it technically means that the iPhone's data plan is unavailable. Since both default U.S. iPhone service providers require you to carry a data plan at all times, the error doesn't usually reflect a permanent loss of cellular data service -- unless, of course, you simply haven't paid your bill, in which case you also can't make or receive calls or texts.
Manually Editing APN
The Access Point Name or "APN" for a network is analagous to user names with which you log in to websites, social networks and instant messengers. In some instances of iPhone usage -- such as if you "unlock" your device and use it in another country -- you manually enter this information within the iPhone's "Settings." Just as is the case entering incorrect log-in information elsewhere, doing so prevents you from accessing data. If you receive this error, contact your mobile carrier to verify the APN you're using is correct.
Prior to Calls
Other instances of this error are more fleeting. If you notice that it only occurs at certain times, you shouldn't be worried. If you use an iPhone 3G or 3Gs, for example -- devices that can't use the Internet while making calls -- this is simply because the data network shuts off during a call and turns back on as soon as the call is finished. Attempt to access the Internet, email or any other Web-based application after the call to confirm the error was indeed fleeting.
If you receive frequent error messages related to a cellular data network but are current on your bill and don't find them to occur just before you make a call, then the error message has nothing to do with you. Rather, your mobile carrier is experiencing data service outages or other sorts of service outages. If the issue becomes inhibitive to you using the device, contact your carrier and ask for further explanation and an estimated course and schedule of resolution.