Contrary to popular belief, WiFi and internet are not the same thing. Local communication between devices (like an iPad and a printer) can occur over a WiFi signal with no connection to the internet. This is sometimes referred to as a Local Area Network (LAN).
A printer with a "Direct Connection" or "Ad Hoc" network is an example of a WiFi network that does not have internet access. Most devices that offer a mode like this can also connect to an existing WiFi network that does have internet access, like a router plugged into a modem.
On an iPad, you must use WiFi to connect to the internet since iPads do not have an ethernet port and can only gain access to the internet through a wireless network.
Read more about this and how to print when a more traditional network will be unavailable in our blog.