How does Boyle's law relate to a bicycle pump?

simply describes the relationship between the pressure and volume of an enclosed gas when Temperature remains constant. That relationship, usually expressed as ##P_1## ##V_1## = ##P_2## ##V_2##, just means that the product of pressure x volume remains unchanged as either or both are changed.

Since pressure x volume remains constant, for example, doubling the pressure on an enclosed gas will reduce its volume to 1/2 its previous size. Tripling the pressure will reduce its volume to 1/3, and so on. Alternatively, if you double the volume available to an enclosed gas, pressure is halved.

Boyle's Law is a hand bicycle pump. By pushing down on the piston, the volume of the gas decreases, the molecules are now having more chances of collisions with the interior walls of the pump and this increases the pressure of the air inside so that it is forced into the tire.

http://everythingscience.co.za/grade-11/07-ideal-gases/07-ideal-gases-03.cnxmlplus