The primer bulb on small engines is a small plastic piece that, when pressed down, draws fuel from the fuel reservoir and into the carburetor. The carburetor is a part of the engine that mixes fuel and air together to make a combustion. Most small engines will not start if the carburetor is dry. Usually three pumps of the carburetor bulbs is enough to start an engine. If the primer bulb is not working, you may need to troubleshoot it.
Inspect the carburetor bulb for cracks on its face. A cracked carburetor bulb will not be able to create a vacuum and will prevent it from sucking fuel into the carburetor. Replace it according to the owner instructions.
Check the ring around the primer bulb to see if it is cracked in any way. The ring holds down the carburetor bulb and seals it.
Inspect the primer line for the primer pump and check for any cracks or debris. The primer line will need replacing if it is damaged in any way.
Inspect the connection of the primer bulb line going into the carburetor. Make sure it is properly connected and sealed and that there are no leaks.
Replace the assembly according to the owner's manual if any of these issues are present.