A celebratory dance sometimes performed in basketball by players after making a critical shot in the game. The dance is usually done immediately after making a shot that is a tiebreaker near the end of a close game.
The performer would hop from side to side, with his legs in a saddle position, and his arms torqued in a manner as if he was carrying something big below his waist - in this case, his balls. The movement is done to emphasize the look of carrying something big, hence the term "big balls dance."
1. Although popular among basketball players, the big balls dance has been looked down upon by the NBA as seen by the recent fines given to Eddie House ($25k) and Josh Smith after displaying it as a way to celebrate their potential game winning shot. (youtube for reference)
2. Damn, that my nig, the black mamba, just did the big balls dance against dem Spurs, lulz.