Two Trees of Valinor
The Two Trees of Valinor are Telperion and Laurelin, the Silver Tree and the Gold that brought light to the Land of the Valar in ancient times. They were destroyed by Melkor and Ungoliant, but their last flower and fruit were made by the Valar into the Moon and the Sun.
Creation and destruction
The first sources of light for all of Arda were two enormous Lamps, Illuin, the silver one to the north and Ormal, the golden one to the south. These were cast down and destroyed by Melkor. Afterward, the Valar went to Valinor and Yavanna sang into existence the Two Trees, silver Telperion and golden Laurelin. Telperion was considered male and Laurelin female. The Trees sat on the hill Ezellohar located outside Valimar. They grew in the presence of all of the Valar, watered by the tears of Nienna.
Each tree was a source of light: Telperion's silver and Laurelin's gold. Telperion had dark leaves (silver on one side) and his silvery dew was collected as a source of water and of light. Laurelin had gold-trimmed leaves and her dew was likewise collected by Varda.
One "day" lasted twelve hours. Each Tree, in turn, would give off light for seven hours (waxing to full brightness and then slowly waning again), so that at one hour each of "dawn" and "dusk" soft gold and silver light would be given off together.
Jealous Melkor enlisted the help of the giant spider-creature Ungoliant (an ancestress of Shelob) to destroy the Two Trees. Concealed in a cloud of darkness, Melkor struck each Tree and the insatiable Ungoliant devoured whatever life and light remained in them.
Again Yavanna sang and Nienna wept, but they succeeded only in reviving Telperion's last flower (to become the Moon) and Laurelin's last fruit (to become the Sun). These were assigned to lesser spirits, male Tilion and female Arien, after the 'genders' of the Trees themselves. This is why, in The Lord of the Rings, the Sun is usually referred to as "she" and the moon as "he".
However the true light of the Trees, before their poisoning by Ungoliant, was said to now reside only in the Silmarils.
Because the Elves that first came to Valinor especially loved Telperion, Yavanna made a second tree like it to stand in the city of Tirion where the Vanyar and Ñoldor dwelt together at first. This tree, named Galathilion, was identical to Telperion except that it gave no light of its own. It had many seedlings, one of which was planted in the isle of Tol Eressëa (named Celeborn).
In the Second Age, a seedling of Celeborn was brought as a gift to the Númenoreans -- that was Nimloth, the White Tree of Númenor. It lasted through the vast majority of the realm's duration, but when Sauron took control of the island he had king Ar-Pharazôn chop it down.
The Two Trees of Valinor existed at a time when the only other source of light were the stars (which had been created for the Elves' benefit by Varda from the dews collected from the Two Trees). When three Elven ambassadors were brought to see Valinor for themselves, in order that they Elves might be convinced to come to Valinor, it seems that the Two Trees affected them most significantly.
In particular Thingol is said to have been motivated in the Great Journey by his desire to see the Light of Valinor again (until he finds contentment in the light he sees in Melian's face). Also in later times, the Elves would be divided between the Calaquendi who had seen the light of the Trees, and the Moriquendi who hadn't, with the former group explicitly superior in many ways.
In the Second and Third Ages, the White Trees of Númenor and of Gondor, whose likeness descends from that of Telperion, have a mostly symbolic significance. They stand both as symbols of the kingdoms in question, and also as reminders of the ancestral alliance between the Dúnedain and the Elves.
Light as a concept is full of symbolism. Tolkien, as a Roman Catholic, would certainly have been exposed to the significance of light in Christian symbolism. Trees were of special importance to Tolkien - in his short story "Tree and Leaf", which in a sense was an elaborate allegory explaining his own creative process, the protagonist, Niggle, spends his life painting a single Tree.
The Trees are just another appearance of the recurrent 'gold and silver' concept of the legendarium. They are created after the lamps Ormal and Illuin, and from the trees themselves, Sun and Moon are created.
Both Telperion and Laurelin are said to have been given many names among which are the following: Telperion was also named Silpion and Ninquelótë while Laurelin was also given the names of Malinalda and Culúrien.
In early writings of Tolkien (see: The History of Middle-earth) Telperion's names were Silpion, Bansil and Belthil.
"Yet even as hope failed [...] Telperion bore at last upon a leafless bough one great flower of silver, and Laurelin a single trait of gold." - The Silmarillion