What is the significance of the Two Lamps?

Question

Before the trees, as I remember, there were two giant lamps that lit the world until Morgoth smashed them. Were these in any way supposed to be the Original Lights of the World when the Children of Ilúvatar woke, and where did the light come from to light these Lamps?

Answer 1

History of the lamps, from the generally reliable Tolkien Gateway:

After the Valar entered the world, there was a misty light veiling the barren ground. The Valar took this light and concentrated it into two large lamps.

Aulë forged great towers on which to place the Lamps, one in the furthest north, Helcar, and another in the deepest south, Ringil. Varda filled them with light and Manwë hallowed them.

In the middle of Middle-earth, where the light of the Lamps mingled and the vegetation of Yavanna was richer, was the Great Lake and the island Almaren, where the Valar first dwelt.

The lamps were destroyed by an assault by Melkor. Their fall was cataclysmic: The symmetry of Arda was destroyed as the weight of the lamps broke continents and their fire burned the land, such that the original design of the Valar was undone forever, including Almaren. The Valar did what they could to hinder the damage and their Enemy and his hosts fled back to Utumno. As they didn't know the time and place of the Children of Eru, they were afraid to rend the Earth again.

The TL;DR version: basically it went like this.

• Valar: Let there be light!
• Melkor: RARGH! Kill! Smash! Destroy!

The lamps were made to light the world, and the light in them came from Varda, aka the famous Elbereth/Gilthoniel.