There are two simple answers to that question as it refers to gases, and one general answer as it refers to any matter in general. First, the general: pressure is a force exerted over an area. It is a "push" on a specified place. As far as gases are concerned, pressure is a result of the many collisions that gas atoms or molecules make with the walls of their container. Finally, since neither of these very clearly explains air or atmospheric pressure, we might add that air pressure may be likened to the force exerted by the earth's gravitational attraction for a column of air above any specific area, such as your head, or the surface of water in a beaker.

Air pressure is normally measured with an instrument called a barometer.