A Team Aerial Counter is when you, well, counter a Team Aerial Combo!
Now the thing about an Aerial Counter is that it is completely luck based.
Essentially, what you have to do is press the exact Arrow direction + A that your opponent presses when he starts the Team Aerial Combo.
So if your opponent hits Up arrow + A, then you have to press the same commands to counter the attack. But you don't know that he hit those buttons so it's a guessing game. The game gives you 15 frames to make a counter. 60 frames is equal to 1 second. So this gives you an idea of how fast you have to be when pulling the counter off. You'll know the exact moment to counter when you see the screen flash.
You have a 1/3 chance to get it right. Your choices are Up arrow + A, Down arrow + A and Left arrow + A or Right arrow + A.(The game does not differentiate between Left and Right arrow in air combos so it doesn't really matter which direction is pressed)
If you have trouble, then find a buddy who will call out what buttons he is going to press before he starts the Team Aerial Combo. That way you can be ready to counter it.
I hope this has given you a better understanding of what Team Aerial Counters are and how to perform them. If you have any questions then feel free to ask.