In the video some water has been added to a soda can and the can with the water was heated using the the small heater. The water inside the can boils forming water molecules in the gas phase.

As the water vapor escape out the top of the container molecules of oxygen and nitrogen (the air) are swept from the container. Eventually only water in gas phase remains in the can, besides the water still boiling.

When the can is removed from the heat, and inverted into water, atmospheric pressure crushs the can.

Why is the can crushed? Since all of the air has been removed from inside the can while the water was boiling, when the can is inverted into the water, the water vapor inside the can is quickly cooled. All of the water vapor inside the can condenses leaving a vacuum inside the can (nearly a vacuum anyway). Inside the can pressure is a very low. Outside the can the pressure is at atmospheric pressure. Because there is very little pressure inside the can, the external pressure crushs the can to try to make the pressure inside the can equal to the pressure outside the can.