Take a straw and suck some water into it. Then hold it over a sink or container with your finger firmly covering the top. The water will remain in the straw. When your finger is not on the top of the straw. Air pressure pushes down and up the straw through both openings, and so is balanced.
Gravity then makes the water fall.
But if you block off the top of the straw, then air pressure can only push from the bottom, and it is stronger than Earth's gravity, so it keeps the water in the straw. Then blow across the top of the paper. The paper rises. This is because moving air has less pressure than still air. By blowing over the top you move the air above the paper and then the higher pressure below pushes the paper up.