Erin's uncle sent a pamphlet provided by the Philadelphia Yearly Meeting to explain this to those who are not familiar with Quakerism and the Quaker traditions.
"From it's beginning the Religious Society of Friends has stressed the conviction that marriage is a binding relationship entered into in the presence of God and of witnessing friends...
The wedding itself is a meeting for worship, held after the manner of Friends, within which the marriage takes place. The bridal couple enter the meeting and take their places at the front of the room. In giving themselves to each other, they eliminate the custom of the bride being given away by her father. No third person pronounces them husband and wife because Friends believe that God alone can create such a union and give it significance. Neither a bridal party nor an exchange of rings is necessary to Friends' procedure although both have become customary today.
In an atmosphere of quiet and reverence during the period of worship, the couple rise. Taking each other by the hand, they make their promises, first the groom and then the bride...
When the couple are seated again, the marriage certificate is brought for them to sign. Then someone who previously has been asked to do so reads the certificate aloud...
The meeting then continues in silent waiting upon God while those assembled share in the worship through prayer and meditation or through spoken messages.
The person chosen to close the meeting [with the shaking of hands] may, if desired, first make opportunity for the bridal party to withdraw. Those present are asked to sign the certificate as witnesses to the marriage...
Many Quaker marriage certificates, handed down from generation to generation, have proved to be valuable historical records. Today, as well, the certificate becomes a cherished possession in the new home recalling the reverent attitude of worship with which the marriage began and the company of loving friends who took part in it."