The message you are getting means that you have not made peace with the router on your home wifi set up.
The fan symbol at the top left shows the signal strength your pad sees from the network, but does not mean you have yet reached the Internet.
Go into settings, wifi, and see if it sees your network, and if it does, is there a checkmark next to the network name. I am guessing no.
The easiest step is to 'forget' that network, and start over.
Have the pad search for available networks. When it finds yours, tap the network name. The pad will then ask for your security password. Sometimes this is the password you set on your router. Sometimes this is the security key that is assigned by your router. Enter the key, and the system will attempt to join the network. When it does, a checkmark will appear next to the network name.
Until you get past the security, you are not 'in'. The pad will remember that network and security, so in the future you will not need to repeat the process.