'I am a servant of the Secret Fire, wielder of the flame of Anor.
While on anchor watch last night I came across an abstract in Morgoth's Ring which reminded me of this thread. It is a piece that was written quite late on by Tolkien when he was attempting to rearrange many of the earlier pieces he had already written, and which subsequently became the Silmarillion. Some of these later writings I struggle with, because to me, Tolkien was trying to take the myth and magic out of the creation of his world and fit it more in line with modern science's view of the creation of our own world. This piece does still fit in quite nicely with that which had already been written, however, and does give an insight into Tolkien's view of the Secret Flame.... Morgoth's Ring p379
As a shadow Melkor did not then conceive himself. For in his beginning he loved and desired light, and the form that he took was exceedingly bright; and he said in his heart: "On such brightness as I am the Children shall hardly endure to look; therefore to know of aught else or beyond or even to strain their small minds to conceive of it would be not for their good." But the lesser brightness that stands before the greater becomes a darkness. And Melkor was jealous, therefore, of all other brightnesses, and wished to take all light unto himself. Therefore Iluvatar, at the entering in of the Valar into Ea, added a theme to the Great Song which was not in it at the first Singing, and he called one of the Ainur to him. Now this was that Spirit which afterwards became Varda (and taking female form became the spouse of Manwe). To Varda Iluvatar said: "I will give unto thee a parting gift. Though shall take into Ea a light that is holy, coming new from Me, unsullied by the thought and lust of Melkor, and with thee it shall enter into Ea, and be in Ea, but not of Ea." Wherefore Varda is the most holy and revered of all the Valar, and those that name the light of Varda name the love of Ea that Eru has, and they are afraid, less only to name the One.
To me, this later part is what Gandalf was speaking of when he mentions the Secret Fire.
Some of what continues is slightly changed from what occurs in the Silmarillion, but Varda added this holy light to the Two Trees as well as hallowing Feanor's Silmarils.
For those of you still with me at this point, it mentions here how Melkor lost his own brightness and became darkened. Varda had given a portion of this light to Arien, the Maiar fire spirit who guided the Sun. Jealous of this light, Melkor chose Arien to be his spouse, but she rejected him, warning him that the fire was something he could not have, and which would burn him. Melkor ignored this warning and ravished Arien, and as she had told him, the light did indeed burn him. His own brightness was darkened, and from then on light pained him.