It helps you detect sensor dust spots or other blemishes prior to printing.
The sensor dust will usually be in the same place on every image, so you can set the slider to show these. On some images you may want to push it further to ensure other imperfections have not been missed. But basically it’s just an aid to using the spot healing tool which will work the same, blending away spots, with or without visualize invoked.
Adobe probably uses a Laplace transform on the image. This is a technique to detect edges. In your image you can see that it is sensitive to noise in the image as noise can look like edges to this algorithm. And yes there is only one dust particle there, the person who tried to convince you otherwise is incorrect. You can generally recognize actual dust particles by their donut shape. Basically the edge of the dust particle gets enhanced by the algorithm but not the middle, leading to the donut shape.
The fact that noise in the image (which absolutely every digital image has contrary to popular belief) can lead to contrast in the laplace transformed image is the reason why there is a threshold slider next to the visualize spots checkbox. If you play with it you'll see it will determine how much of the noise you see vs the actual dust spot.
P.S. another place where this transformed image is used is in the sharpening preview. If you hold your alt/option key while sliding the masking slider you'll see the same image and you can help make it determine where you sharpen. You generally do not want to sharpen a featureless sky for example as it only leads to increased noise, so you want to make sure the sky is black in that image.