FRATERNITATIS A.·.A.·. is one of two things. There is one mystical group called the Eternal and Invisible Order, often also called the Great White Brotherhood, which goes by A.·.A.·. and exists to guide humanity along in its evolution. There is also an outer order which calls itself A.·.A.·., whose initial purpose was, ostensibly, to facilitate corporeal admission to the inner order and help individuals attain to their Knowledge and Conversation of the Holy Guardian Angel (KCHGA). In both cases, noone outside the order is ever told what A.·.A.·. actually stands for. Some have theorized that it stands for Argentum Astrum (the Silver Star), but there's good evidence to indicate that this is not correct.
It is a shame that anyone ever set up an outer order with the same name as the inner, for all outer orders run the risk of degredation, often described in A.·.A.·. terminology as losing the Spirit but keeping the Letter. It can get very confusing, trying to discern between the two entities, but if the inner order is as flawless as they are presented as being, then there may well be some function served by this similarity of naming.
In any regard, the best information on both orders is available at the A.·.A.·. Home Page.