Flame of Anor

The Flame of Anor is some element or power obscurely referred to by Gandalf who claimed to wield it, in the face of Durin's Bane. Only speculation can be done about its meaning and nature.
Anor is the Elvish name for the Sun, and so literally the "flame of Anor" would be the light of the Sun, which originated in the fiery fruit of Laurelin, one of the Two Trees of Valinor. Alternatively, the "flame of Anor" may refer to Gandalf's possession of Narya, known as the "Ring of Fire".
The expression might metaphorically refer to some power wielded by the Wizard, as a Maia and servant of the Flame Imperishable; with the pure light of the Sun as an antithesis of the "dark fire" of the fallen Balrog.