Alight can have many different meanings.
It might mean something that is on fire. It might also mean you are getting off something after it has stopped moving, like a horse or a train. It could also mean you are coming onto something after a flight, as in "see the bird alight on that branch".
Candles used to be the main source of light for people long ago before light bulbs and electricity were invented. Candles are made out of a piece of string, or wick, which is surrounded by wax.
When the candle is first lit you set the wick on fire but once the wick is burning it melts the wax, so after that first few moments the candle burns the wax not the wick.