Awakening Values (AVs) are a replacement for the Effort Values (EVs) in other games. They’re the same concept, but work slightly differently. Whereas IVs are (kind of) set in stone from the start, AVs can be changed at any time.
As with IVs, Pokémon can have AVs in each of the six key stats (HP, Attack, etc.). Initially, the AVs for each stat will be 0. To increase a Pokémon’s AVs, you feed them stat-boosting candies. 1 AV equates to 1 point in the corresponding stat, independent of Level. A total of 200 AVs can be gained in one stat; unlike EVs, there is no shared cap.
Benefit of AVs
It should be pretty clear how big of an effect AVs can have. If you’re not convinced, consider a Level 1 Pokémon. Now feed it enough candies so it has 200 AVs in all stats. All of its stats will then become 200+, which is comparable to some Level 100 Pokémon! Hmm, time to stock up on candies and give your Pokémon diabetes…