Flame of Anor
The Flame of Anor was a mysterious power claimed by Gandalf in the face of Durin's Bane. It is nowhere else referred to, and so its particular meaning remains unclear. Anor is 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. Gandalf seems to be referring, then, to the power he gains as a servant of the Lords of the West, in defiance to the corrupted darkness of the Balrog.
Alternatively, it has been suggested that Gandalf is referring here to Narya, the Ring of Fire that he bore. This idea certainly fits with the notion that he was the 'wielder' of the Ring, and that it had a fiery character. However, it seems highly unlikely that Gandalf would want to reveal his ownership of a Ring of Power - a matter of utmost secrecy - to one of his greatest enemies.