Our sages say that one who marries can erase past sins. The reason
for the evocation of Yom Kippur is that a wedding marks a new beginning
with a chance for a clean slate. In fact, the wedding day is the first
time that groom dons a kittel, a white garment that is
traditionally worn on Yom Kippur. Rather than dragging in negative
baggage from their pasts, the bride and groom enter into marriage with
hope for a building a new future together. On
the day of the wedding, the Ashkenazic custom is for the bride and
groom fast, for it their personal Yom Kippur. They are set to start a
new life with a clean spiritual slate and get forgiven for all 
sins. They also include the order of Viduy, like on Yom Kippur in their prayers.
For the actual marriage ceremony under the chuppah, the groom wears a kittel, a white garment that can also serve as a traditional shroud. The white symbolizes purity and cleansing from sin, and the reminder of mortality is also meant to inspire proper spiritual thoughts, which is why men wear kittels on Yom Kippur. Some grooms put it on before walking down the aisle, while others opt to only don it upon arriving at the chuppah. Members of Chabad wear a black coat over their kittels. Though they do have outdoor chuppahs, the reason for the coat is not the weather but an attempt to cover the kittel. Sephardim do not have the custom of wearing a kittel at the chuppah, so perhaps the Chabad custom is some type of compromise position of wearing it but not overtly showing it.
What of the bride? Of course, a traditional brides dons a white gown, and while that is not mandated by Jewish law, it fits in well with a parallel drawn between the bride and the high priest during the Yom Kippur Temple service. Traditionally, brides remove all jewelery prior to walking to the chuppah. According to the book Ta'amey Haminhagim [The Reasons for Customs] as the high priest would only enter into the Holy of Holies in the all white linen garments rather than the garments of gold, the bride enters into yichud with her husband without her extra adornments.
Click on the links below to learn more about various aspects of the Jewish wedding and marriage halachos
the procession to the chuppah,
standing-under-the-chuppah The wedding of Yitzchak and Rivka
Birchas Hamazon: the-grace-and-round-2-of-the-seven-blessings
