Partial Vacuum
How it works:
Burning paper heats the air molecules in the bottle, setting them in motion so they begin to repel each other. Some of the air escapes through the gaps between the egg and the neck of the bottle. When the flame goes out, the air molecules cool down and attract each other.
The air from outside the bottle rushes into it, but the egg blocks its path. The pressure of the air molecules outside the bottle is so strong that they literally push the egg inside the bottle.