We pull the cord that I guess would get the pump up and it started pumping,
I would think the rope is to pull the pump up with. It is probably tied to the pump. I doubt it would be a Briggs and Stratton motor with a pull start rope.
Lots of times; pits like yours fill with sand. This can stick the pump into the bottom of the pit if they didn't set it up on blocks. Usually when this happens, the sand will also stick the impeller so it can't start turning when the motor tries to start. This can burn one up quickly, so a little maintenance might be in order for the pit.