Have you ever wondered how a candle works? If you haven't, think about it for a while. Why does it take so long for the wick to burn down? Why does it need a wick at all?
When you light the wick on a candle, the heat melts the wax in the wick and at the top of the candle. This liquid wax is drawn up the wick by capillary action, getting hotter and hotter until it turns into a gas. This gas mixes with oxygen in the air and is ignited by the flame that melted the wax in the first place. The heat of the flame melts more wax and this wax too is drawn up the wick. Then the whole process repeats itself until all the wax has been burnt.
So why does a candle need a wick? If you try to light a lump of wax you can melt the wax but that is just about all that happens. The wick does the important job of keeping the molten wax in the heat of the flame long enough to vaporize. Liquid wax does not burn. Wax has to be in its gaseous state before it will ignite and burn. If you look at the wick of a candle that has already been used you will see that it is all burnt and black. What you are seeing is loose, powdery carbon and soot, held together by the wax that was traveling up the wick when it was blown out.