A glass candle is an object made out of dragonglass (obsidian), made in the old Valyrian Freehold before its destruction four hundred years ago in the Doom of Valyria. Allegedly, using the power of magic they could be made to burn with light.Several glass candles are preserved in the Citadel in Oldtown. The night before an acolyte attempting to join the Order of Maesters says his vows, he must spend an all-night vigil attempting to light the candle. Secretly, this is actually impossible, and the point of the exercise is to impress upon the new initiate that even with all of their knowledge, some things are impossible - and to stress that the maesters do not believe in magic (even acolytes who are not studying the "higher mysteries" (magic) must undergo this ritual).
With the return of dragons to the world in the possession of Daenerys Targaryen, their link with magic seems to be strengthening the ability of long-dormant magical powers and objects in the world. Glass candles which had not burned in centuries are now said to be burning with light.
In the books
In the A Song of Ice and Fire novels, Valyrian glass candles are said to be powered by magic. The light they give off does strange things to colors, making bright colors such as white, yellow, or red shine unusually brightly, while dark colors such as blue or black turned as dark as night (basically, it had the same effects as a modern blacklight). It was rumored that glass candles could be used to observe far away events and communicate with other glass candles over vast distances (similar to a palantir from J.R.R. Tolkien's The Lord of the Rings). The Citadel of the Maesters possesses four surviving glass candles, one green and three black.
- Glass candle at A Wiki of Ice and Fire (major spoilers from the books)