Symbolism of the Chuppah from Wikipedia
In a spiritual sense, the covering of the chuppah represents the presence of God over the covenant of marriage. As a man's kipa (skull cap) served as a reminder of the Creator above all, (also a symbol of separation from God), so the chuppah was erected to signify that the ceremony and institution of marriage has divine origins. The "chuppah" may also represent the home of Abraham and serve as a reminder that he was a foreigner in a strange land, looking for the place God had promised to him. Before going under the chuppah the groom covers the bride's face with a veil, known as the badeken. The origin of this tradition is in the dispute of what exactly is the chuppah. There are opinions that the chuppah means covering the bride's face, and that by this covering the couple is getting married. Thus, some are strict to make sure that the witnesses will see the covering, for them to actually be considered as witnessing the marriage. The groom enters the chuppah first to represent that it is like his home or garment. When the bride then enters the chuppah it is as though the groom is providing her with shelter or clothing, and he thus publicly demonstrates his new responsibilities toward her.