What is online inverter?

"Online", as applied to inverters, means that the inverter is supplying the load in an operational state, i.e. "online". The inverter stage is running from the battery, floated from the rectifier, generating voltage, which is synchronized to the alternate source.

Contrast this with "Offline" inverter, which means that the inverter stage is not running, or that it is in a standby state. In this case, loss of power causes the inverter stage to start, and to take the load. There is going to be a glitch in the output when this happens, usually of a few line cycles.