Is it showing full signal for your normal carrier? If not it might be in "emergency calls only" mode but showing the signal level for another carrier. If you go to the mobile data settings you should be able to see what network you are on, if it's not visible somewhere else. Networks do have outages, so this isn't impossible.
If you have access to another phone or another SIM it might be worth swapping to see whether the problem is with the handset or the SIM. SIMs do fail sometimes.
If the SIM seems to be OK and you've tried trivial things like rebooting then it's probably best to speak to your carrier.