I suggest people watch the following video from beginning to end to have a better appreciation of their A/T, what the ATF exactly does, how some 'universal' ATFs are taboo, and how it's a good idea to stick to OEM or big-name brands of the correct ATF-type .
The guy is an Amsoil advocate but this video is not solely about selling their product. In fact, he insists that people take care of their A/T by using only the best stuff from reputable brands (Mobil 1, Valvoline, Castrol, and their own, among others). Needless to say, OEM fluids of the correct type should also be on the top of your list.
The A/T is by far the most complex piece of machinery in a modern vehicle, period. And in the middle of every bits of gears, pumps, pistons, clutches, etc., is the ATF. Commensurately, the ATF has a very difficult job to do and you typically don't want to skimp on it.
In a nutshell, the ATF has the following critical tasks:
1. Hydraulic fluid - It should be thin enough to function as a hydraulic fluid to push gears, pistons, clutch packs, and for the torque converter (a hydraulic pump) to work
2. Friction modifier - Different car manufacturers who designed and made the A/T requires a certain 'grippyness' for clutch packs to engage. Suffice to say that using the wrong ATF will have an adverse effect on the life and/or shift quality of the A/T
3. Coolant - ATF is constantly circulated around the A/T to take away generated heat. This heat is released through an external cooler or a compartment in the radiator.
4. Lubricant - This is self-explanatory. Without it, the gears and clutch will eat each other up in no time