The push you never notice
The air around you presses on every square centimetre of your skin with the weight of about a kilogram. You never feel it because it pushes equally from all sides and from inside you too. It becomes noticeable only when it is unbalanced: your ears popping in a lift, a suction cup clinging to a window, a tin can crushed when the air inside is pumped out.
That push is pressure: force spread over an area. It is measured in pascals, one newton on each square metre, and the air at sea level exerts about a hundred thousand of them.
Where it comes from
Look inside the cylinder. Every particle flies in a straight line until it hits something, bounces, and flies off again. Each bounce off a wall gives the wall a tiny shove. Alone, one shove is nothing. Together, billions of billions of them every second, on every part of the wall, add up to a steady outward push. That is all pressure is: the drumming of particles on a surface.
Try it: switch on Wall hits and set the volume to Squeezed. Then set it to Full and compare how busy the walls are.
Squeeze it
Push the piston down and the same particles have less room. They cross the space more quickly and reach a wall more often, and there is less wall to spread the hits over. Pressure goes up. Halve the volume and the pressure doubles, as Boyle found in the 1660s by trapping air in a bent glass tube. This is why a bicycle pump gets hard to push near the bottom of the stroke and why a sealed bag puffs up in an aeroplane cabin, where the air outside is thinner.
Heat it
Heat the gas and the particles move faster. They hit the walls more often and each hit is harder. Pressure goes up again, this time without the volume changing. A sealed can heated in a fire is a bomb for exactly this reason, and a car tyre reads higher after a motorway drive than in the cold garage.
Put the two together and you have the gas law: pressure times volume grows in step with temperature. Everything from a steam engine to a breath obeys it.
Not just gases
Liquids push too, and their pressure grows with depth, because each layer carries the weight of everything above it. Ten metres of water adds the pressure of the whole atmosphere again, which is why divers must rise slowly and why dams are thickest at the base. Solids push back as well: a sharp knife cuts not because you press hard but because the same force is squeezed onto a tiny edge, and pressure is force divided by area.