The WiFi connection is only available for the Lifeprint 3x4.5 printer. All other Lifeprint printers are Bluetooth only. The default connection mode for any Lifeprint printer is Bluetooth, even the 3x4.5 printer.
Specifically for the 3x4.5 printer, if your phone is close to your printer, the Bluetooth connection will be active and used exclusively by the App. Once the WiFi is configured on your printer, it will become active once the Bluetooth is no longer connected. When connected to WiFi, print requests from your app will now be sent to the Cloud and passed on to your printer at home, meaning you can print from anywhere. The Wi-Fi connection will also report the status of the printer, so you will know if it is out of paper or runs into other issues.