Kissing under the mistletoe is a tradition that finds its roots in Norse mythology and the ancient Celts
To druids living in Gaul, Britain and Ireland, mistletoe symbolized perpetual life. It was believed to have mystical properties as it was found on the sacred oak trees. As the plant grows on tall branches, it appeared as though the gods had dropped it there from heaven. The fact that mistletoe remained green all winter while its host tree looked lifeless also added to its magical status.
Gallic people called it "the one that heals all". A sacred plant to them, it was believed to have medicinal and magical powers. Actually poisonous, mistletoe does have a long history of being used for medicinal purposes in many cultures. Druids also used it to cure illnesses and regarded highly its curing powers.
Based on those mystical beliefs, people started hanging mistletoe on the doors of their houses and barns to ward off the evil spirits and bring luck and fertility to the household. Kissing a guest that would enter the house under a bunch of mistletoe was believed to bring him good luck.
In Norse mythology, there is a famous story about Frigga and her son Baldr. There are many versions of the myth, but they mostly agree that Baldr the Beautiful was destined to die a young man. As the winter solstice grew close, his mother, Frigga goddess of love and beauty, had a vision of her son's death. To prevent it from occurring, she ran into the forest asking every living thing to never harm him. The earth, the air, the fire, the water, the trees and the animals vowed to not take part in his demise. However, she overlooked the small and insignificant mistletoe bush.
Baldr grew to become the favorite of many gods. Loki, a jealous rival, cunningly used an arrow carved out of mistletoe to kill him. Learning of his death, Frigga cried so much that her tears became the white berries of the plant. She then vowed that mistletoe would never again be used as a weapon and declared it a symbol of love and peace adding that she would place a kiss on anyone who passed under it and forever protect them.
These and other stories were eventually integrated into Christian traditions. In middle age Europe, mistletoe was abundant at the beginning of winter and people started offering it as a gift and decorated their homes with its greenery. It gradually became part of Christmas and New Year traditions, while maintaining its meaning of love and peace.