Think of a clown juggling balls. The more balls he has in the air, the more skillful he is. Now extend that to multitasking.

'to keep or have many balls in the air' is an informal expression,that refers to trying to do several different things at the same time or putting separate tasks together.

"Many balls in the air" is an idiom basically saying that there are many things happening at once, or many responsibilities at once, etc. When multitasking, one tries to "keep all the balls in the air at once". Hope this helps :)