When your Briggs & Stratton engine won't start but has plenty of gas, a clean carburettor and air filter, and a good spark plug, then you will need to make sure the flywheel magnet is working. The flywheel magnet rotates past the magneto next to the flywheel and creates an electric current that travels to your spark plug and creates a spark. Over time the magnet can begin to wear out and not provide the proper magnetism the magneto needs to create an electrical current.
Remove the metal housing (that contains the pull start rope) that is bolted over the flywheel on the top of the Briggs & Stratton engine. Use the proper sized wrenches to remove the bolts holding the housing in place.
Rotate the flywheel so the magnet is facing one side of the mower engine---so it isn't against the magneto.
Press a 1/4 inch flathead screwdriver against the magnet. Let go of the screwdriver. If the magnet can hold the screwdriver in place then it is OK; if the screwdriver drops then the flywheel magnet is worn out and you will have to replace it.
Remove the two screws that hold the magnet into the side of the flywheel with the screwdriver. Push the new flywheel magnet into place and tighten it in.
Replace the flywheel cover and tighten it back into place.