Cock and Ball Torture
Cock and ball torture, commonly abbreviated as CBT, is a somewhat generic term for sexual play involving some degree of pain applied to the male genitals specifically.
The simplest reason to explain the obvious why question may be that at the extremes of sensation, the lines between pleasure and pain blur. CBT can provide (for some men) levels of ecstatic pleasure far greater than any "normal" experience. As a side note: many men also enjoy testing, pushing their limits physically and in a ritual or spiritual aspect as well.
For some people this includes light bondage, flogging, play piercing and other related "torture" of the male genitals, some people may also include light play such as clothespins and elastration play as well.
Ball Torture
In the context that BME uses the term "ball torture", it almost always refers to testicular torture and testicle skewering and so on—play piercing of the testicle itself (versus surface play piercings in the scrotum or shaft). Some include temporary elastration, testicular crushing, scrotal stretching, and other modifications and play in this definition.
See Also
More pictures on cock and ball torture can be found on BME in the CBT - Cock Torture Gallery and Scrotal Torture Gallery (sorry, members only link).