This means they don’t have their own network, but rent space on the network of a larger network (AT&T, T-Mobile, Sprint, Verizon, Sprint and so on).

What has likely happened is that some settings got fudged up (automatically - Apple doing you a favor) and your phone now thinks its using AT&T's service. Turn your phone on and tap the Phone app, as if you were going to call a person.

Open the dial pad so that you can enter your voicemail system's number.