Okay, difficult to explain without showing, but I'll try.
When you walk barefoot, you tend to put your heel down first, followed quickly by the ball of the foot/toes, pressing down on the ball of the foot and lifting the heel as you move forward again.
When in heels, you have to tilt your pelvis slightly forward and put the foot down 'flat' (heel and ball of the foot at the same time). To move quickly and comfortably when walking like this you need to sway your hips slightly as you walk - nothing exaggerated, it's not a big swing, no more than a cm or two. People who sway their arse like Marilyn Monroe in Some Like It Hot are putting it on.
If you try and walk in the barefoot manner, putting your heel down first, you will wobble horribly and probably crack your shoes across the top of the toes in time. You know you're doing it properly if your shoes don't 'gape' on either side of the ball of the foot when you place your foot down.
Hope that makes sense, it's not something I have to think about tbh, it's 'natural' for me in high heels to move that way because I'm used to it.
I'm not advocating heels per se, or saying it's somehow 'better' than wearing flats (I love my New Rock boots just as much as my heels), it's just that if you are going to wear heels, it's a lot more comfy to walk that way, looks less like you're a constipated duck on stilts and gives less wear and tear on your (expensive) shoes! :o