Particles in a gas

The particles in a gas are spread out far away from each other. The particles move about randomly all the time. They move very freely.
If the gas is inside a container, then the particles hit the walls of the container as they move around. Each time a particle collides with the wall, it causes a tiny force. There are huge numbers of particles colliding with the wall, and all these tiny forces add up. We call this gas pressure.

Less space, more pressure

What happens if you squeeze the gas particles into a smaller space? There are the same number of gas particles, but they will now hit the walls of their container more often. This makes the gas pressure greater.
The same thing happens when you squeeze more gas particles into a space. This is what happens when you inflate a football. You push more air into the space inside the football. There are more air particles inside the football, so there are more particles and more frequent collisions with the walls of the football. This increases the pressure inside the football.

Higher temperature, more pressure

If you warm a gas, the particles have more energy so they move about more quickly. They hit the walls of their container more often. This increases the pressure.

The collapsing bottle experiment

You cannot feel them, but the particles of air around you are bumping into your skin. These moving air particles cause pressure on you and on everything else on Earth.
If you use a vacuum pump to pump air out of a plastic bottle, there are fewer air particles inside the bottle. The frequency of collisions of particles with the walls on the inside of the bottle is less.
On the outside of the bottle there are lots of air particles colliding with the walls of the bottle. The pressure on the outside is greater than the pressure on the inside, so the walls of the bottle are pushed inwards.