No Air Inside: By filling the bottle completely and sealing it, you remove all the air. This means there is no air pressure inside the bottle pushing down on the water.

Atmospheric Pressure: The air outside the bottle is constantly pushing on every surface with a significant force (about 14.7 pounds per square inch at sea level). This pressure pushes up on what is now the bottom of the upside-down bottle.

The Pressure Imbalance: The situation looks like this:

• Force trying to push water out: Gravity (pulling down on the mass of the water).

• Force keeping water in: Atmospheric pressure (pushing up on the bottle's base).
  Since there's no counter-pressure from inside, the external atmospheric pressure wins, holding the water in place.

The Role of the Plastic Bottle: Plastic is flexible. Unlike a rigid glass bottle, the plastic will often deform. As the water tries to move down slightly, it creates a tiny partial vacuum inside. The stronger outside air pressure then squeezes or "crushes" the bottle slightly inward until the pressures are balanced. This is a visible proof that a pressure imbalance exists.