Blue Balls is a real condition! The "correct" term for blue
balls is epididymitis, which is an inflammation of the epididymis.
In simple terms blue balls occurs when the epididymis get blocked up with sperm that have left the testis but not the penis. The vas deferns are the conduit for the sperm from the testis to the urethra. When they get blocked you get pain. Why blue balls and not "swollen balls," well maybe the connotation is that you balls have the "blues", or maybe its because with all that swelling some of the blood flow is restricted enough to cause some blueing of the area because of pooling blood.