Air is composed of molecules which are not linked to each other and that move freely in space. Air molecules trapped in a volume occupy all of the available space and rebound against the surfaces they meet (sides, objects, walls..). When the volume decreases or increases, the molecules move closer or farther apart from each other. The number of collisions/rebounds is directly related to the pressure.
Two experiments with one or two syringes allows for the introduction of pressure and the relation between pressure and volume.