The couple exchange garlands of flowers. This is a common part of Indian weddings, where the ceremony is called varmala or jaimala, and represents a proposal by the bride and acceptance by the groom.
It also represents their new unity, blessed by nature. In Hawaiian weddings, the bride and groom typically exchange leis. The families may also exchange leis with the couple. Leis represent the love and respect you have for the person you are giving it to, and the unity of the new family.