A bicycle tire pump works just like any other
simple force pump such as a bilge pump or lift pump. There is a valve blocking
the flow of air out of the pump to the atmosphere while on the downstroke, and
another valve stopping the flow of air from the tire to the pump cylinder during
the upstroke.
Tire pumps come in a huge variety of shapes and styles but this
is one of the most common varieties.
Some modern bicycle pumps deliver air
on both the downstroke and the upstroke by having an additional set of valves.
This reduces the time it takes to fill the tire.