You would archive a device because you are no longer using that FitMachine to monitor that piece of equipment. By archiving a device you remove it from the active devices on your dashboard and the action of archiving is irreversible. This means it will no longer appear with the rest of your fleet of FitMachine in the List View or the Device Admin View.
You can see all the devices that have been archived on your dash by selecting the archived tab instead of the active tab (shown above). You can archive a device from the Equipment Detail View or from the Device Admin View.
Equipment Detail View (above) and Device Admin View (below)
The below is the warning you will receive before archiving a FitMachine.