The practice of genuflection, or bowing on one knee, typically the right, is not as old as some might suppose. Traditionally, it dates back to the 16th Century, at about the time of the Protestant Reformation. It signifies humility and self-abasement in the presence of the Real Host. Faithful Catholics and members of the Anglican Communion genuflect when in the presence of Christ's presence in the Eucharist, although genuflection may have ties to the secular practice of physical obeisance before earthly lords and kings.
Yet we might place genuflection in a much longer tradition of physically arranging the body during prayer. This practice dates back certainly to the very early church and even to the Old Testament, when people occasionally kneel in prayer. This would contrast with the standard Jewish position of standing to pray, and was used to express a particularly fervent or heartfelt petition. By the fourth or fifth century, kneeling had become the posture of private Christian prayer, while standing remained the norm for public and corporate petitions before God.
Modern genuflection might then represent the presence of individual piety in the midst of common faith. We hold nothing more personal than our bodies, and moving them in response to the presence of the broken body of Christ, and in reply to the words that affirm his physical sacrifice, symbolically connects us to Christ's emptying of self in this world and upon the cross- whether we bow on one knee, or two, or in the Eastern fashion prostrate ourselves entirely.