A2DP: I saw these jargons all the while, although I seem to have used it, never bothered to know what it was! Me being me, this was unacceptable!
So, here it is - A2DP stands for "Advanced Audio Distribution Profile". The Bluetooth Core has a protocol stack, over which, devices can add different profiles for each service that they provide. A2DP was introduced for "streaming", superior quality stereo music over traditional bluetooth technology.
There are other profiles as well, the ones that most of us have experienced - HeadSet Profile (HSP), HandsFree Profile (HFP), Human Interface Device Profile (HID) etc.
Interested in knowing more? I suggest reading this on Wikipedia.