The Two Trees of Valinor were two trees created by the Valar to give light to Valinor. Before the sun and moon were created, the Trees were the primary source of light in the continent. (Middle-earth didn't have any light besides stars.) The Trees were made by the song of Yavanna and watered by the tears of Nienna, giving them great power.
Telperion was the "male" tree. It gave off a silver glow and had dark leaves that were silver on one side.
Laurelin was the "female" tree. It gave off a golden glow and had gold-trimmed leaves.
The Elf lord Fëanor captured some of the light of the Trees in his masterpieces, the Silmarils. It is rumored that he got the idea from Galadriel, as her hair was said to have absorbed some of the radiance from the trees.
When Melkor decided to show his hand, he enlisted Ungoliant, the giant spider, and with her help drained the Two Trees of their light, killing them and plunging Valinor into darkness. Yavanna claimed that she could heal the Trees if she used the light in the Silmarils, but Feanor was attached to his precious gems. Not merely that, Melkor had stolen them anyway. Yavanna sang to the dead trees, hoping to revive them, and the Vala Nienna watered them with her tears, but it was no use. They managed to coax a single white blossom from Telperion, and a single golden fruit from Laurelin. These were placed in the sky to serve as sources of light for all of Arda, with the flower becoming the moon and the fruit becoming the sun. This is why the sun is often referred to as "she" and the moon as "he" in The Lord of the Rings.