Without a model number of your mower, I can only give you general information about your lawn mower.
Usually when this happens the engine runs on the fuel you pumped into the carburetor with the primer, but can't draw any fuel through the carburetor, so it dies.
This is usually an indication that the engine sat through the winter with untreated fuel in it and has stopped up the fuel and air passages inside the carburetor.
Draining and cleaning the fuel bowl on the carburetor will sometimes get the engine going. Many times the carburetor has to be replaced before the engine will run.