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1.
When, in the heat of summer, your balls are soaked in sweat.
I wish I had air conditioning - there sure is a lot of ball soup going on down there.
by Chintz November 05, 2004
 
2.
When testicles become sweaty due to hot conditions (Clam Chowder is the female equivalent).

Perspiration on male genitalia after prolonged activity or hot conditions.
Can you turn up the AC? I'm sitting in ball soup over here.

I get wicked ball soup after a good run.
by brisket79 August 25, 2013
 
3.
(noun) created when your balls sweat so much that a layer of sweat, dust, and residue creates a foamy broth which then coagulates into a hard shell on your balls and/or taint.
We need to get an air conditioner, I'm tired of getting ballsoup every summer
by Intrepid Dissent July 24, 2010