Just like the fog, the feeling of movement is present throughout the poem. Sometimes it pauses ("it sits looking"), but there's always a constant progression occurring in terms of the fog's presence and movement. And since the fog is fused with the imagery of a cat, we also see all of these moves in a way that looks rather catlike.
Line 1: First the fog "comes" on those "little cat feet." It's the beginning stage of the sort of movement we get in the poem. It's the approach and the anxiety that comes along with it while we wait. Although there's a line break between Lines 2 and 3, we understand that some time has passed there since the fog looks different by Line 3. So, although we didn't "see" the movement, we know it's occurred within that line break.
Line 3: Then it "sits looking," which suggests we have a short pause in the actual "moving" part of the fog's movement. But, even as it sits, we understand that it could be on the move again at any moment. It's unpredictable and potentially powerful.
Line 6: By the end, it "moves on" and leaves us feeling somewhat relieved. We can't move with the fog at this point since it's no longer over our heads, but we nonetheless watch its departure and wonder where it will go next.