"Blue balls" is a slang term for vasocongestion in the testicles or vulva. It refers to the pain or discomfort after sexual arousal or stimulation. This simply means that the man's testicles and penis (or a woman's vulva) have filled with the ejaculatory fluid, blood and increased pressure needed for an ejaculation and they are now trapped within the penis (or vulva). He/she may experience pain or discomfort due to the increased pressure. Men and women can experience this vasocongestion but it seems that males complain more of this condition. This condition does not necessarily lead to pain.
To deal with the pain and/or discomfort a person can either masturbate to orgasm or allow the arousal to fade with time. If these are not an option, an ice pack or warm compress or even a shower or physical activity can alleviate the discomfort.
TeenHealthFX wants you to understand that the discomfort or pain does not imply that you need to have sex with a partner. It is not necessary for a person to have an orgasm with a partner. If anyone tells you that they have "blue balls" and needs to have sex because of their suffering, please know that this is NOT true.