For simplicity reasons, and in the vernacular of every day people (non chemists), you can think of the fire triangle. DrCMS is right since he is getting more technical than most people do or really need to.
Heat, fuel, and the 3rd thing is what the aluminum foil is depriving. The 3rd part has already been mentioned once in this thread.
Think of the combustion of methane (this isn't what the candle is burning, but it's simple).
CH4 + x --> CO2 + H2O
x is the thing that aluminum is depriving. Can you figure out what it is from the equation?