When organic materials such as yard trimmings and leaves break down in a lake or stream, the decomposition process uses oxygen from the water. In a natural creek system, the amount of organics introduced into the water is limited to the leaves of plants and trees in the immediate creekside. Due to this limitation, a natural creek can easily balance itself, and the leaves and debris that make it to the creek have a minimal impact on the ecosystem.
In an urban setting, large quantities of organic debris can be flushed through the storm drains and into the creek. These excessive amounts of organic material can easily overwhelm the creek's ability to buffer itself against the depletion of oxygen that occurs when those materials decompose, which can harm or even kill fish and other wildlife that depend on the oxygen in the water for survival.
Additionally, large quantities of yard waste can potentially clog the storm inlet, which could cause flooding in the street or neighborhood. Storm drains are for rainwater only, and should not be used to dispose of anything other than stormwater.