In many cultures, religious denominations, and families, virginity until marriage is considered sacred. Virginity is typically associated with purity, innocence, virtuosity, and thought of as a gift to a future marital partner. Loss of virginity prior to marriage is equated with being a used, cheapened, damaged, or otherwise unappealing (keep in mind this isn't the case for all people are waiting for marriage to have penetrative sex).
Women are often held to this standard much more so than men (a great example of the double standard). In some cultures, a non-virgin woman is unable to get married, and often times in those cultures, there are no options for women other than being a wife.
Purity balls are a logical extension of the abstinence-only approach in Western culture (particularly North American). If you're unfamiliar with purity balls, the following clip provides a pretty superficial glimpse. Keep in mind that it's from a mainstream American network, so it's a bit sensationalized.