Summary
If your opponent hits you and you recover from Hit Stun while in the air, you will automatically perform an Air Recovery. If you do not hold any direction on the controller, you will bounce up and slightly back a very short distance the instant you recover. If you hold Back on the controller, you will bounce up the same height but bounce backwards a greater distance. If you hold Toward on the controller, you will still bounce slightly up but bounce forward a small distance instead.
Flipping for Safety
This is one of the main new systems in Marvel Vs. Capcom 3. Whenever you recover from Hit Stun in the air, Air Recovery automatically kicks in and learning how to use this will be one of the major changes in terms of gameplay between MvC2 and Marvel Vs. Capcom 3.
Air Recovery allows you to escape a lot of resets and traps because, now when you recover in the air, you have choices on which direction your character will travel. For example, She-Hulk can easily set you up in the corner with a purposefully abbreviated Air Combo so that she lands when you recover and can catch you with her Heaven Throw Hyper Combo, which grabs people out of the air. However, now that you can perform an Air Recovery so that you bounce forward, you can escape these sorts of traps and force more of a guessing game on the opponent trying to set you up.
Strategy Corner
By default, everyone will be used to holding Back on the controller when getting hit in the air, so as a result most people will begin their Marvel Vs. Capcom 3 career performing backwards Air Recoveries constantly. Unfortunately, smart players will start to take advantage of this and set up traps, typically through Air Throws, to 
your Air Recovery.
So heed this word of advice: learn to start varying your Air Recovery direction now. If you start growing accustomed to learning to vary between going forward or backwards with the Air Recovery, it will make you that much harder to predict which way you are going. Thus, it will be a lot harder to punish the Air Recovery. So start getting used to going both directions now.
Also, during the start of the Air Recovery, you are actually invincible for a small period of time. That means old tricks that were resets in the air will no longer work in Marvel Vs. Capcom 3. In MvC2, for example, Storm could perform an Air Combo and cancel her move into an Air Dash behind your character to combo you from the other side and, if you didn't block correctly, she would reset the Damage Reduction and get even more damage on you. Now, those tricks won't work as easily because, not only does the little flip in the air on Air Recovery throw off your positioning, but the invincibility will allow you to react and block these sorts of resets.
The invincibility is very short, but it is enough to allow those ready to react to it and take advantage of the invincibility. However, you can attack the instant you perform an Air Recovery. If you do this, you forfeit all invincibility that you gained from the Air Recovery. So if you are being struck in the air, make sure you are not needlessly pressing any buttons while getting hit (such as mashing Special to counter an Aerial Exchange) or else, during Air Recovery, you may accidentally do a move you did not intend and then get hit by another move because you've lost all your invincibility.