In a natural, undeveloped environment, rainfall from storms falls on the ground and evaporates or is absorbed into the soil. The water that is absorbed is "cleaned" as it moves through plant material and the soil layers. This water replenishes the groundwater and provides baseflow for streams.
In an urban, developed environment, like Philadelphia, rainfall from storms falls on the ground and runs off from impervious surfaces (e.g., concrete, asphalt, buildings, etc.) and flows into the sewer system. This water is what is referred to as stormwater runoff or stormwater or runoff. Since this water can't be absorbed into the ground and take part of the natural water cycle, it needs to be managed. Stormdrains on the street and other surfaces allow the stormwater into the sewer system that PWD builds and maintains.