[I always liked this post because it is silly, and reminds me of the silly walks episode in Monty Python. At the same time, it is absolutely true, and useful, and something to practice until it becomes second nature. With best wishes - your editor.]
You are almost invisible. You are wearing your best tourist clothes. Your camera is in your hand or around your neck. You have spotted a subject standing in a doorway a half-block away. You imagine how far from the subject you’ll be when you take the shot; if you take the shot. You pre-focus, either by aiming the camera at a similar distance, or with hyperfocal distance, or whatever method you want for the situation.
There are people walking behind you and people walking towards you. As you approach your subject you evaluate whether you can quickly snap this shot or not. Your shutter speed is set to 1/150th of a second (which is the best you can manage in this light) or 1/1000th if you are lucky. And just as you hit your mark the camera goes to your eye and you stop, in mid-step and snap the image and without removing the camera from your eye, continue with your walking.
You have got your shot, and you were stock still when you took it. Only problem, as you stopped momentarily for no reason that was apparent to the guy behind you, he bumps into you – not expecting you to stop. This is the stutter-step. All street photographers use it; and having someone bump into them from behind is common. You mumble, sorry, and continue on your way.
Again, the idea is that you want to pause for just that brief moment while you squeeze the shutter and continue on as if nothing happened.

In this case, I've stopped for the split second, the subject hasn't.