The online mode is the preferred mode of operation is a WiFi network is around.
In online mode, the clock is connected to the internet directly via a WiFi router, all the communication between the configuration device (your phone with the installed app or a computer with the opened website) and the clock is done over the internet. There is no direct connection between the configuration device and the clock. The only exception is the connection process, during which is the clock for a while connected directly to the configuration device.
The clock doesn’t need the internet to operate, the internet serves only as a source of time and provides a settings interface. When the internet goes down, the clock continues to run, it just isn’t synchronized and is not accessible in the configuration apps. Once the internet is available again, the clock reconnects to our cloud and continues in time sync as usual.