You can think of a flame as being like a kind of tent. Heat melts the candle's waxy fuel, and turns it into a gas. This fuel gas floats away from the wick to fill the inside of the flame's tent. Outside the tent are oxygen molecules from the air. Where these two gasses meet--at the surface of the tent--is where the fiery chemical reaction takes place. This is called the "combustion reaction zone" of the flame, and it glows a delicate blue color.
Sometimes, however, the fuel molecules don't burn up right away. They clump together to form particles called soot, which then swirl around inside the body of the flame without actually burning. As they swirl, heat from the reaction zone can make this soot begin to glow a bright orange or yellow color.
The reaction zone at the surface of the flame's tent provides the blue color of the flame. The yellow color comes from hot soot, churning around inside.
Eventually this soot will probably enter the reaction zone and burn blue like the rest of the fuel. If the reaction zone is incomplete however, or not very efficient, the soot can escape the flame without burning at all. Outside the flame, the soot cools quickly to black and drifts away. What do we call this unburnt sooty fuel? You guessed it. Smoke.