In the Greek Orthodox church, a Koumbaro (or Koumbara, in the feminine) is the official sponsor and chief witness for the couple. In addition to being present at the altar, this person is responsible for the exchanging of the Stefana and rings.
The Stefana are traditional wedding crowns used in the Greek Orthodox wedding ceremony, which are used in the ceremony to signify the couple as the king and queen of their home. The Stefana are bound by a ribbon, which symbolizes the bond between the couple, and their union before God. The crowns are exchanged three times between the bride and groom by the Koumbaro(a), ultimately landing on different heads. (In other words, the bride's crown will wind up on the groom's head and vice versa). This is done to seal the union, making the two as one.
Following the gospel reading, which tells of the wedding at Cana of Galilee where Christ turned water into wine, the bride and groom drink a small portion of wine that has been blessed. The Common Cup signifies that from this day forward, the couple shall share all aspects of their lives; joys and sorrows, triumphs and hardships. Whatever the challenge, the burden shall be cut in half, and whatever the joy, it shall be experienced twofold, as the couple now shares everything equally.
The circling around the table signifies the promise of the husband and wife to preserve their marriage bond until death parts them. The bride and groom wear their crowns, and the Koumbaro(a) follows them, ensuring that the crowns stay in place, and holding the ribbon so that the symbolic bond is secure. The ceremonial walk is especially significant, as these are the first steps the couple takes together as husband and wife. They are essentially supported by God (the priest and the Holy Bible, which rests on the table), light (the candles upon the table), and their loved ones (their Koumbaro/Koumbara).
One big difference is that the bride and groom don't exchange vows or say "I do." Their bond is solidified through the exchanging of Stefana and walking around the altar. There is a gospel reading (John 2: 1 ‑11), but it is handled solely by the priest instead of a family member. Unlike a Catholic ceremony, there is no Communion for attendees, although the bride and groom do share from the Common Cup. Also, you may notice Greek attendees crossing themselves slightly differently. The sign of the cross is made with the index finger, middle finger, and thumb (representing the Holy Trinity), and the sequence goes up, down, right, then left (in the Catholic church, it goes from left to right). This is done to signify the right hand of God, where Jesus is said to be seated. However, wedding guests may cross themselves with whatever method they are familiar.