GASES can be modelled as small particles (representing the molecules or atoms of the gas in question) flying about in all directions. (This simplified model is called an ideal gas.) As these particles strike the walls of their container so they exert a force on the container pushing it outwards. This force per area is the pressure exerted by the gas. This animation shows gas particles being introduced into a cubic container to illustrate the concept. If the dimensions of the cube are unity then the force on a wall represents the pressure of the gas.
PARTIAL PRESSURE: when there is a mixture of two or more gases, then each gas can be (for ideal gases) considered separately. The total pressure will be the sum of the pressures of each constituent gas. This can be understood by watching the animation and seeing how particles of each colour effectively "ignore" each other and behave as if they were the only inhabitant of the container.