I’m still trying to get a handle on the idea myself, but I can give you something of an answer. Motion in stillness sometimes refers to the internal movement of chi while outside the body seems still. For example, during nei gung (internal practice) a practitioner might be standing or sitting still, but internally, there’s a sensation of great movement as the chi circulates. This practice probably contributes to stillness in motion, which is often talked about in tai chi chuan, but I’m not entirely sure how they’re related.
Stillness in motion is very similar, but while the outside body is moving, inside the thoughts are calm and still, the energy is smooth and refined. It’s very useful for combat because when the mind is calm, it’s easy to mobilize the right response. Having a calm mind gives the fighter the time and ability to assess the situation in a very relaxed way so that they can muster a response very quickly and be able to do exactly the right thing at the right time.
Also, if the center is still, then everything external (arms, legs, waist) can spin around the center like an axis. In a bicycle wheel, the axis has to stay still in the center (revolving, but centered). If it moves all over the place, then the spokes of the wheel can’t be well connected and the wheel won’t work, it will collapse. Similarly, if the center of the body-mind can be still, then thoughts and movements coordinate together, making for efficient combat applications.
We can also see what is not stillness in motion by observing push hands or sparring situations. There’s usually the guy who’s usually fairly calm and relaxed who often “wins” and doesn’t seem to get upset when he “loses” and doesn’t really seem fazed by much. This is pretty close to stillness in motion. Then there’s the guy who gets pushed off his root, gets angry about it and fights back with a series of wild motions that aren’t well executed and gets pushed over repeatedly until he calms down. This is not stillness in motion. It’s more like motion in motion—anger and frustration can have the energy of a wild blaze—powerful, but not controlled, and easily neutralized by someone who can maintain their own sense of stillness amidst the maelstrom.
The closest Western idea that I can think of for relating stillness in motion to combat is the phrase “Revenge is a dish that’s best served cold.” When the heat of anger and passion is stilled or distilled, it can manifest in a potent cold calm. Let me be clear that I’ve never heard of a tai chi master advocating revenge, and think focusing on revenge is a super bad idea myself. Whatever the situation though, staying calm in all situations is key to stillness in motion and is especially useful in combat.
Having a quality of stillness is also useful for avoiding combat in the first place. Who’s more likely to start a fight: the relaxed guy sunning himself on a beach towel, or the jittery one on the corner glaring at everyone who walks by? Moreover, if you are the guy on the beach towel, how likely is the jittery guy to even notice you, much less try to pick a fight? He’s most likely scouting for danger, so if you seem safe-still-calm-quiet, then you don’t even register on his radar. People who are agitated tend to attract other people who are agitated. So stillness in motion is useful for both combat and for avoiding combat.