A glass candle is a candle made of obsidian. Historically they burned, but they have not been reported to burn in recent memory. One green and three black candles were brought to the Citadel from Valyria a thousand years before the Doom of Valyria. It is unknown if all glass candles are alike, but the ones found at the Citadel are tall and twisted. It claimed that when the glass candles burn the sorcerers could see across mountains, seas and deserts, give men visions and dreams and communicate with one another half a world apart. 
The night before an acolyte of the Citadel says his vows, he must stand a vigil in a vault with nothing but the three black candles and no other light permitted. They must spend the night in darkness unless they can light the candle. According to the maesters, it is to show that even with all the knowledge one has acquired, there are still some things that are impossible.
A Clash of Kings
A Feast for Crows
Leo Tyrell reports that the green glass candle is burning in Marwyn's study. There is a black glass candle burning Marwyn's study on the Isle of Ravens when Samwell Tarly arrives there. When Sam asks Alleras they knew he was coming he nod at the glass candle.