Activations are usually complete within 30 minutes, but can sometimes take 24 hours.
It's recommended that you restart your phone occasionally to find out if the activation has worked, because the phone will probably not recognise it until you do,
However, you should also check, if you haven't done so already:
that giffgaff normally has good service in your area, which you can check by putting your full postcode in at https://giffgaff.com/coverage-and-service#coverage
that there are no known temporary faults, by repeating the full postcode (not just a town name) at https://giffgaff.com/coverage-and-service#network