The priming system on most lawn mowers sits on the fuel line heading back to the tank, or the purge line. The rubber bulb, which generally sits on top of the carburetor, uses suction to draw fuel into the carburetor. When the primer function stops working on the mower, items like dirt or grass are often blocking the fuel from getting sucked into the carburetor.
Unscrew the air filter box and slide it away from the side of the engine. Unscrew the choke or throttle plate to gain access to the carburetor. Unhook the fuel lines and watch for gas to flow out. If gas flows out, the problem lies somewhere else, like in the carburetor, which only a professional should service.
Check the condition of the main and secondary fuel lines if no gas is reaching the carburetor. Remove the fuel cap on the mower and tilt it, carburetor side up, to gently drain all fuel into the container. Brush and wipe the fuel cap clean. Check the vent hole for plugs and unclog with the bristles.
Unscrew the primer bulb and remove it from the top of the carburetor. Replace the primer bulb if it's cracked, or if its airtight seal with the carburetor seat has been broken. Lift the fuel filter from the tank, drawing it into the tank opening, with the metal hook.
Pull the filter off the end of the main gas line. Check the condition of the main and secondary fuel lines from the tank to the carburetor. Replace the hoses if they're cracked, yellowing or brittle.
Refill the mower's tank with gas and check the primer function again. If the primer still won't work, and the engine won't start, the carburetor will need servicing and cleaning from a professional.