Device status is what gives you a quick dashboard of the state of your devices. The "status" column itself is often the most useful, but Deviceplane also provides some other useful information about your devices in the Devices page.
Since most devices cannot be expected to have perfect network connectivity, the "status" column is not a realtime column. Rather, it checks whether a device has been online within the last two minutes. If you shut down a device, and it still shows as online, this is the likely reason why.