The air filter cleans any incoming air of particulate matter. If this matter enters the engine, it could scour the bore inside the piston and ruin an engine. However, these foam filters tend to get dirty quickly, and once they get too dirty, they'll stop working properly. Air will enter in short bursts as the engine tries to suck it through the dirty filter. These filters will need cleaning after every 8 to 12 hours of operation, and they require replacement seasonally.
The fuel filter sits at the bottom of the tank and traps any impurities in the fuel. If these impurities make it to the engine, they could damage the carburetor and the combustion chamber. Dirt, grass and other matter may enter the fuel tank during a refueling stop, as a careless operator knocks it into the tank. This matter will float in the tank and eventually get sucked against the filter, partially blocking it. These filters also need regular cleaning, usually after 15 to 20 hours, and they should be replaced seasonally.
If any object was small enough to pass through the filter, it may reach the fuel hose and get lodged inside. This will allow only a small amount of fuel to pass, which may make the engine sound like it's surging. Due to impurities in the fuel, these fuel hoses will clog over time, as the gas erodes the quality of the hose. These fuel hoses need replacing every other season, or more frequently if bad or old gas was used or if gas was left in the mower during storage.
Eventually some debris and dirt will find its way to the carburetor. The carburetor also uses a small screen on the inlet fuel passage to trap any material before it can damage the mixing and measuring sections inside the carburetor. When this screen gets dirty, it will only allow a small amount of gas to surge through to the carburetor. Carburetors need a thorough cleaning at the beginning of the season.