Clouds are formed when water droplets in the air cool and then collect on dust particles. In this experiment, the smoke provided the dust particles from the match.
You will see vapors form inside the jar this is because the warm water and the match heated the air. The warm air rose to the top of the jar and touched the cool air from the ice cubes. When the warm wet air meets with the cold air it forms a cloud of water droplets. This is what you see with our clouds outside. Clouds are filled with water droplets and when they get to many of those droplets then it rains.
Releasing the pressure after the bottle was squeezed cools the air inside the bottle. Squeezing the bottle changes the temperature: the amount of air within the bottle is constant, but squeezing the plastic bottle changes the volume of the gas.
Expanding the bottle causes a lowering of the air temperature – in this case, enough to cause the water gas to form a liquid – the cloud.