It’s because the candle doesn’t burn solid wax; it melts the wax into a liquid, then boils* the liquid into a gas, then burns the gas. However it’ll only boil the liquid into a gas if the temperature is high enough, and that’s only possible near the flame, so it’s limited by the amount of liquid wax the wick is able to pull up (through capillarity).
You can make it burn for longer or shorter by changing the wick thickness.
*it’s actually a bit more complicated than just boiling; a lot of the molecules in the wax get broken by the heat into smaller and more volatile molecules (pyrolysis). But “boiling” explains it well enough for most cases.
You missed that the wax only “boils” (I would have said vaporizes, but as you said, boils is close enough) at the center of the flame where it is drawn up by the wick. Otherwise, this is correct.
Fun bonus detail, visible flames are usually burning gas. Burning solids look like hot embers. The flames from a wood fire are usually burning smoke. You can actually re-light a candle by smothering the flame and quickly lighting it’s smoke tail on fire.
Yes to all this but if you don’t want any smoke, use the unburned end of the same match you previously lit the candle with to quickly push the wick tip down into the pool of wax to extinguish it. Lift it right back up again while the wax is still melted so it’s ready to light later.
