The fuel filter is clogged or the carburetor needs to be cleaned and/or adjusted.
grab it around the throat (carburetor) and choke it until it starts.
you tube how to clean a mower carburator.
There are a couple of reasons why a lawnmower will not stay running or not getting fuel. The carburetor may be clogged up or the lawnmower gas may have water in it.
Look for a clogged fuel filter or a faulty spark plug. Another possibility is that the carburetor needs to be re-set or cleaned.
A bad, stuck or dirty float needle inside the carburetor.
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More than likely it is a gas problem. Either the filter is clogged, the gas tank has something in the bottom clogging the outlet, you are out of gas, the carburetor is gummed up or if it is a riding mower it might be the solenoid on the bottom of the carburetor is not working properly. If you haven't used it in a while the chances are it is in the carburetor itself. You can verify it is a gas problem by spraying some carburetor cleaner into the carburetor while it is trying to die and see if it continues to run on the cleaner.
dirty carb causing gas not to flow to keep it running... youtube has videos... it would take a long time to type it all out.
if it starts and runs for just a few seconds then dies it is generally a carburetor issue. clean or replace the carb and that should solve your issue.
If you are talking about the bulb button it is a primer to get gas to the carburetor if the mower has not run for awhile. Usually not needed to restart a warm mower.
If your lawn mower is pulsating, it may mean that it is not getting enough fuel and the carburetor may need cleaning.
They are for the fuel solenoid shutoff