A part in mistletoe folklore comes from Norse mythology. As the story goes, when the god Odin’s son Baldur was prophesied to die, his mother Frigg, the goddess of love, went to all the animals and plants of the natural world to secure an oath that they would not harm him. But Frigg neglected to consult with the unassuming mistletoe, so the scheming god Loki made an arrow from the plant and saw that it was used to kill the otherwise invincible Baldur. According to one sunnier version of the myth, the gods were able to resurrect Baldur from the dead. Delighted, Frigg then declared mistletoe a symbol of love and vowed to plant a kiss on all those who passed beneath it.
Technically, it traces back to ancient Norse mythology. At least, that's where the mistletoe's association with romance came from. It really picked up in the 18th century, when it became a tradition for British servants to kiss under a mistletoe. The tradition spread from there.