Something so incredible that it makes your balls ache just thinking about it. Women can experience something incrediballs in her breasts (especially if they are ball-shaped) or by cupping the balls of a man she is with when something incrediballs happens.
I saw that chic cupping your balls last night, what happened?
We saw a man with a coon-skin cap and it was incrediballs!
A beard that is so remarkable and must be photographed, documented, or even commented on, in order to label it with significance; usually for later conversation about how epic the beard was.
Dude! Do you remember that Incredibeard that we saw at the mall the other day?! That guy must have been growing that since 1974!