The fog comes on little cat feet. (1-2)
The speaker is immediately blending elements of nature into one metaphor right from the beginning. We're starting to see an attempt to understand fog through human imagination as the speaker immediately creates an image that we can relate to.
It sits looking over harbor and city (3-4)
It sounds as if the speaker recognizes the enormous size and scope of nature in the context of fog. It's covering "man" and the world he created, emphasizing its power and potential.
and then moves on. (6)
The speaker can't really say where exactly it's moving, just like we can't always explain stuff that happens in nature. Sometimes we can only watch and wait and see what happens next.