AVs are the new EVs, exclusive to LGPE. AVs are obtained by giving a Pokemon a candy (Courage Candy, Health Candy, Mighty Candy, Quick Candy, Smart Candy, Tough Candy). The more you use a specific candy, the harder it is to get an AV. AVs can boost certain stats, to a really high level. Even something that is really low leveled could have stats of a Level 100 Pokemon. You can put a maximum of 200 AVs into each stat. And to answer your other question, AV stands for Awakening Values.
Hope this helped!