The AP adapter essentially is a fake battery that allows the cord to be plugged directly into it. This then removes the need to place the actual battery which carries the weight into the tool, instead, you can wear it on your hip or in the backpack instead.

E.g. if you buy the MSA 220 you can place this fake battery in the unit instead of the actual battery then run the cord to the unit and wear the battery with the weight on your hip or in a backpack on your back.