Home well water systems are designed so the water pump doesn't run continuously. If the pump in your system is doing that, it could be an indication something is amiss.
In a properly functioning system, the well pump pushes water into a pressurized tank containing both air and water. As water enters the tank, the air becomes increasingly compressed. Once a set pounds per square inch (PSI) of pressure inside the tank is achieved a limit switch turns off the pump. When you turn on a tap, the air pressure forces water from the tank, through the plumbing system and out the tap. As the water flows, the pressure inside the pump drops and when it reaches the cut-in point, the pump again turns on adding water to the system. In most home systems, several gallons of water will flow from the pressure tank before the cut-in point is achieved. This saves wear and tear on the water pump since it doesn't run constantly nor does it turn on and off each time you dispense a glass of water or flush a toilet.
If your water pump turns on each time you open a tap, flush or take a shower, then turns off seconds after you stop running the water, you have a water-logged pressure tank. If yours is a modern, bladder-type tank, the bladder which separates the air and water has probably broken and the tank needs replacing. In an older, non-bladder tank, the tank needs to be drained completely or air added using a special fitting and air compressor. Bladder type tanks fail infrequently. Non-bladder tanks need to be de-waterlogged on a regular basis depending on the size of tank and amount of water being used.
At times of high water use, such as when running multiple lawn sprinklers, several people showering in different bathrooms simultaneously or other high-use situations, the pump may not be capable of pumping an adequate amount of water to keep up with the demand and will run constantly until something is shut off. If this is a regular occurrence, consider getting a higher capacity pump or larger well. If high water demand is the exception rather than the rule, don't worry. Things will go back to normal after the peak demand passes.