Gravity does the job. Storm sewer drains are put in low spots along curbs. That way, gravity moves water toward the drain and into the sewers.
Once the water is in the storm sewer, it moves downhill through the pipes. Once again, gravity does the job.
In some storm sewers, however, pumps are also used to move the water.
Rainwater flows downhill along the curb, pulled by gravity. Rain flows toward the storm drain.