The accelerator pump squirts a couple of streams of raw gas into the intake manifold, where, hopefully, it evaporates enough before it gets to the cylinders to keep from wetting the spark plugs and flooding the engine. Pulling the choke knob all the way out allows intake manifold vacuum to go all the way to the top of the air horn and draw gasoline through all the passages in the carburetor, creating a rich enough mixture that the cold engine has a better chance of starting.
More sophisticated carbs like the Weber DCOE series have a small-diameter "starting enrichment" venturi that is opened up by a cable for cold starting, and no choke plates. There's a fast enough airflow through the small venturi to provide a richer mixture for cold starts.
Jerry