The term consummate on its own refers to the idea of bringing something to completion. So when something is truly complete such as a contract, it is said to be consummated.
When it comes to a marriage they are not truly completed or consummated until sexual intercourse occurs between a man and his wife after the ceremony. In some cultures and societies a marriage is not considered a binding contract until it has been consummated with sex. The Catholic Church will even allow any marriage that has not been consummated, regardless of the reason for non-consummation, to be dissolved by the Pope. Also an inability to consummate, or a refusal to consummate a marriage are both probable grounds for having an annulment of ones marriage.
Catholic law recognizes that a marriage has been consummated when spouses have performed between themselves a conjugal act by which spouses become one flesh and by that it is an act that is suitable for the procreation of offspring. Some theologians have even argued that contraceptive intercourse (such as using a condom) is therefore not in itself consummation. But these theories are not accepted by law or widely agreed upon. It is a tradition for the Bride and Groom to have sex on their wedding night, therefore, consummating the marriage. More historically it would have been expected that both were virgins, the bride especially.