To literally have your hard cock so deep in the womans pussy that your balls are pressed up against her pussy lips. Every inch of your dick inside her.
Balls deep has two meanings, the first meaning is in the sexual way of getting your penis all the way in into a vagina and only the balls are left outside, and the second meaning that it is used between homies is when you go really hard into something like doing a good hard workout and feeling it after.
First example in a sexual way: Yo bro I went balls deep on her sister last night.
Second example in a non-sexual way: Yo bro I went balls deep on that workout and all my body hurting now.