The fog comes on little cat feet. (1-2)
The fog comes just as unpredictably as it goes. Change in the poem creeps up on the speaker like those kitty paws and changes the landscape in only six lines.
over harbor and city (4)
Sometimes change can affect many people all at once and we get a sense of this when the speaker mentions the word "city." Of course the effects of change may be different, but here we sense the scope of it.
and then moves on. (6)
Change, just like the fog, doesn't stick around and wait for us to get comfortable. Oftentimes it just shows up, turns things upside down, and then "moves on."