A while back I did a bit of digging through posts in this forum by the Madden devs (when they used to post here) and old EA Sports blog posts to get definitions for all the ratings (along with another OS member, PocketScout; not sure if he still posts here anymore). With that in mind, here's what I've got for AWR:
AWR affects how well the CPU controls a player in the general case, how quickly a CPU player can react to an airborne football, how quickly a CPU player can react to a fumble, the decision of the CPU to fall on the ball vs scoop-and-score, and CPU blockers' identification of the correct defender to block. Since the introduction of the Infinity Engine, it also has some effect on all players - user or CPU controlled - with respect to player balance and footwork.
By-and-large, PRC replaced AWR as the relevant rating for intelligence checks in many defensive situations when it was introduced in Madden 07, such as recognizing a draw play, biting on playaction, biting on pump fakes, and general reaction time to a running play.
Until Tiburon decides to release a full guide for all the ratings in their game - which they absolutely should, there's so much noise with respect to what the ratings and the sliders in the game actually do - take the above for what you will. For what it's worth, I once had a WR on my team in the preseason of a Madden 13 CCM with an AWR of 20, and often times he wouldn't even make an attempt to catch a well-thrown ball as if he never saw it lol.
It's my opinion that at this point in Madden's life AWR is _way_ overvalued in the player's default OVR rating calculation, based on that information I gathered on what it does.