On a window a.c. unit the mode that is Dehum what is that for? Or the purpose of it?

That refers to the "Dehumidifier Mode".

Air conditioners work by pulling air out of your home via return ducts, cooling the air, and then recirculating it throughout your home. But sometimes all your home needs is dehumidification. When the humidity finds its way inside our homes, sometimes all you need is the movement of air.

Ceiling fans are a common choice in homes with temperatures around the upper 70ºs. A ceiling fan can reduce the temperature you feel in the room by up to 10º in some cases.

A dehumidifier’s core function is to remove the moisture from the air. In order to do this, the dehumidifier pulls the air into the system, cools it, heats it, and dispels the moisture into a bucket or a drainage system.

To learn more, see this Comfort-Pro.com blog.

Tip! Techlicious shares Tips on How to Select the Best Room Air Conditioner.

Monday, June 27 2016
Source: http://www.comfort-pro.com/2015/03/do-air-conditioners-dehumidify/