A lawn mower uses a fuel filter to purify all incoming gas. If this fuel didn't get cleaned, the impurities, such as dirt or grass clippings, would ruin the carburetor, or worse, the combustion chamber. Unfortunately, these fuel filters can also get clogged easily if a large piece of grass gets sucked up against the mesh screen. This will immediately cause a loss in fuel to the carburetor and the added fuel on the choke setting will allow the mower to operate. The fuel filters on most lawn mowers need seasonal replacement.
Two fuel lines connect the tank to the carburetor and they allow the gas to travel freely as the engine needs it. However, just like the fuel filter, these hoses can get clogged from foreign objects, which can cause the mower to run only on full choke. However, these fuel lines will still degrade naturally over time due to the nature of the gasoline. Once these lines degrade, they will no longer let in enough fuel, so replace them at least every other season.
A dirty carburetor is likely the main cause of this problem. The inlet passages on the carburetor also contain a mesh screen as an extra layer of protection to the most sensitive parts inside the carburetor. Just like the fuel filter and fuel lines, if this screen gets blocked, the fuel reaching the carburetor won't be enough for normal operation and the full choke mode will allow enough fuel in. The carburetor will need servicing at least every couple of seasons.
The carburetor needs to work smoothly and efficiently for the mower to run without the choke on. When the carburetor needs cleaning, it will need to be completely removed from the engine and disassembled. The parts will need an overnight soaking in a carburetor cleaner bath. After a thorough cleaning, install a carburetor rebuild kit, which will add many years to the life of an old carburetor. Allow a professional to make carburetor repairs if you don't feel qualified.