Jumping State
In Marvel Vs. Capcom 3, there are three ways you can end up in the Jumping State. The first and very obvious way is by simply jumping from the ground. The second way is actually not as obvious: any time you recover in the air with a Tech Flip, you will be in Jumping State. So, for example, if you ever get struck by an opponent's Launcher but they do not follow up with any attacks, when you recover in the air you are considered in Jumping State. And the third way you can end up in Jumping State is whenever a new character comes into the game as a new Point Character after the current Point Character has been defeated or Snapped Out.
While jumping, you can perform as many actions as your Jump will allow you to squeeze in until you land. For example, if you jump into the air and perform an air Hadoken with Ryu, after you recover, you can still perform an attack on the way down... or even another Hadoken. Still using Ryu, if you Air Block a move at the height of your Jump Arc, right before you land you can still perform an Air Hadoken before you land. Characters with Air Dashes and Double Jumps can even perform those before they land.
Strategy Corner
It's important to point out that, in MvC2, you were only allowed one action per regular Jump. As stated above, this is different in Marvel Vs. Capcom 3 so you can do as many actions during a regular Jump as you want. This actually means there is no longer the "Guard Break" technique in this game where you could force a jumping character to block a move and then hit them after their Air Block before they land and they can't do anything about it.
Also, in MvC2, Normal Moves that altered your Jump Arc, such as Iron Man's Down + Hard Kick or Wolverine's Down + Hard Kick, would put you in Jumping State even if you performed them during a Super Jump, which allowed you to call Assists after performing these moves. This technique will not work in Marvel Vs. Capcom 3. You retain Super Jumping State when you perform any Normal Moves of this type.
Also for characters that have Double Jumps and Air Dashes, if you perform a Double Jump or Air Dash while in a Jumping State, you actually maintain that state throughout the Double Jump or Air Dash. So if you Double Jump or Air Dash with Chun Li, for example, you can still perform things you can perform normally during a Jump, such as calling an Assist. Also, if you are hit while in the air during a Jumping State and recover in the air, you stay in the Jumping State.