(this is more properly a Chemistry question, not a mathematical one)
The kinetic molecular theory of gasses tells us that gasses behave the way they do because they are made up of molecules in motion (kinetic molecular).
The easiest way to picture this is to think of bouncy balls in a container, all moving around and bouncing off the walls endlessly.
"Pressure" is the force of the bouncy balls hitting the walls. The more times they hit the wall, the more frequently they do so, and the faster they are moving when they hit, the "harder" they hit, and therefore the higher the pressure in the container.
Boyle's Law tells us that if we increase the volume, the pressure decreases, and if we decrease the volume, the pressure will increase.
Think about it this way: If we make the container bigger (increase volume), the bouncy balls will have to travel farther to hit a wall, and therefore won't hit as often. This decreases the pressure (fewer collisions = less pressure) If we make the container smaller, the opposite will happen. More collisions, higher pressure.
The reverse is true, too. If we create more collisions, the container will try to get bigger in response. If there are fewer collisions, the container can shrink.