When you are burning a candle, you are essentially vaporizing the liquid wax into a gas that is flammable. This vapour can then be used as fuel for the candle flame. It is this vaporized wax that fuels all candle flames used with conventional wax-based candles.

If you blow out the candle, you have put out the flame on the wick but there is still vaporized wax that is in the air that can be used. You cannot see this vapour, but it will travel in the same direction as the smoke.

Therefore, as you hold a flame close to the smoke it will light the unused wax vapour that is in the smoke. It will then follow the fuel (wax vapour) all the way back to the candle wick where there will be enough fuel for the candle to continue burning like it was before you blew it out.