In this context, the usage is always plural. I will refrain from an anatomical explanation why this is so. As Nathan and Lolerpops have said, the expression refers to the courage to do something. The wording is common speech, quite informal, but might be considered rude by your grandmother.

Feminists may object to the identification of courage with the capacity to produce testosterone. There are many women in the world who have more balls than some men. http://www.slate.com/articles/news_and_politics/explainer/2010/08/a_ballsy_explainer.html

Balls = courage

Balls refers to testicles, in this case meaning either daring or courageous enough to :)

Balls, used in this sentence, is a metaphoric term or a figure of speech that means COURAGE or GUTS