top dressing a yard
"Top dressing" is the application of compost / soil and sometimes seed mixture to an existing lawn. Note that it is only about 1/4" and is sprinkled on the existing grass. Applying it too thickly will hamper the health of existing grass by blocking out sunlight.
These low areas can be repaired by loosening the soil in the pits and incorporating a quality top soil into the existing soil. Bear in mind the top soil will settle, so mound the soil slightly. Sprinkle a seed mix suitable to your site conditions (sun, sun/shade, dense shade, dry, etc.) and water. overseed into the neighboring lawn to create a "blending" of the new seed and existing lawn. Keep these areas watered to germinate the seed and keep the established grass healthy. You may want to cover these areas with seeding mulch or a seed blanket (available at local garden centers and home stores).