“Blue balls” is slang for the discomfort guys feel in their testicles when they are excited for some time without release.
During sexual arousal the genitals fill with blood. The testicles can increase in size up to 50%. The blood gives the scrotal skin a bluish tinge. That’s why it’s called “blue balls”.
When you orgasm the swelling subsides and goes away. But if you don't come, it can take up to two hours before your testicles are back to normal.
It can cause discomfort, but is not harmful in any way.
Sometimes women too will feel pain in the vulva or general pelvic area if they are excited but don’t come, but this is discussed less often and doesn’t have a name.

: I was very angry when he complained of blue balls.