Okay, let's start with the basics. A parkway is that little strip of grass, trees, or (depending on your neighbors' level of motivation) dirt and weeds between the edge of the road bed and the sidewalk. Although the parkway is technically within the public right-of-way, the adjacent property owner is responsible for its design and maintenance.
Parkways are an important part of the pedestrian landscape for two reasons. First, they provide space for streets trees and other plantings that make the pedestrian environment more comfortable and interesting for walking. Second, they act as a buffer between the sidewalk and the traveled roadway, which increases pedestrian safety.
In practice some homeowners get pretty creative with their parkways, but until last week the only things homeowners were technically allowed to plant without a permit were street trees and lawns. Yawn. With the release of Los Angeles' new Residential Parkway Landscaping Guidelines, homeowners can now plant a variety of "drought-tolerant turf substitute plants," including grasses, a handful of flowers, and even beach strawberries.
Of course, anything more elaborate--including permeable paving or non-plant groundcover--requires a $400 permit, which strikes me as a little questionable. I suppose I understand the desire for landscape regulations within the public right-of-way (e.g. planting a tall hedge can obstruct driver views and hinder pedestrian safety, invasive plant species can create problems for native vegetation), but such a high fee is surely a disincentive for people who might otherwise want to create an attractive quasi-public space in the parkway.
Thus, with the slight fear that I may be outing them to the authorities, I'll introduce you tomorrow to my favorite local parkway here in Woodland Hills.