In order to complete the activation of the SIM card you will need to activate the SIM card with a £10 minimum top up or if you bought a £5 goodybag minimum directly using a credit/debit card or Paypal.
Most of the SIM activations are processed within a few minutes(30), but it can take up to 24 hours in some situations. You can check if your SIM has been activated by logging in "My giffgaff" here http://www.giffgaff.com/dashboard . When the SIM is activated, your purchase will be displayed:
In the "Balance" box if you added credit to your balance In the "Your goodybag" section if you bought a goodybag When your SIM is active you'll also see giffgaff as your network provider.
I also suggest you turn your device off and on again periodically to see if that helps. If your SIM is not activated after 24 hours, then i suggest you contact a giffgaff so they can verify the status of your SIM activation. A giffgaff agent can be contacted by following this https://support2.giffgaff.com/app/ask/Getting-Started/Activating-my-SIM/form/ link , please note during busy times a giffgaff agent can take up to 24 hours to respond to your query.
If activating by topping up credit only, the minimum payment is £10. If activating a SIM by the direct purchase of a goodybag / gigabag, the minimum payment is £5 (if you use a debit card/ credit card/ PayPal) or £10 if you are using a voucher.