BnB stands for Bread n Butter. It's the combo that you should be able to do at least. It's goal is to launch the enemy into the air and then doing an air combo, mostly ending in a throw.
AD stands for Arc Drive. You do an arc drive if you input 41236C in HEAT. The numbers refer to the numpad on your keyboard. 4 is for backwards, 2 for down, 6 for forward etc. C is the 3rd hit button.
The AAD is the AD in BLOOD HEAT, usually a stronger variation of the AD itself.