Place one of the eggs on the mouth of the jar. The egg sits there and does not move. There is a balance between the air pressure pushing down on the egg, the air pressure pushing sideways, and the air pushing up from inside the jar.
Gravity pulls the egg down, but the bottle pushes it up.
Remove the egg and drop two well lit matches into the jar. Observe the egg. Discuss what happened to the egg. When you changed the balance of pressure, the egg moved. In this experiment, you removed some of the air inside the bottle and it is not able to push up with the same pressure as it did before the experiment.