As described by General Wax, candles burn through a cyclic process by which the flame melts the wax, which is drawn up the wick into the flame where the wax vaporizes and ignites, producing heat which in turn melts more wax, repeating the cycle of combustion. The process will continue until the flame is deprived of fuel or air.
Candles are composed of some sort of solid fuel formed around a central wick. The wick is usually some kind of string or cord, often made from braided cotton. The fuel portion of the candle, which makes up the majority of the candle's bulk, is traditionally some kind of wax, but can also be made from paraffin or tallow fat. When the wick is lit, the heat from the flame begins melting the candle fuel which is then drawn up through the wick by capillary action. When the liquid fuel reaches the flame, it is heated into a gas and burned. The burning fuel is what produces the flame while the wick only burns once it extends beyond the flame as the candle burns down. The cyclical process produces a self-sustaining exothermic reaction, allowing the candle to burn at an even rate.