Moving the Black point right (inward) emphasizes shadows and makes the image darker. But you may not always want the shadows to be darker. The Black Point determines level 0. Therefore values to the left of the Black point are black too, and can contain no detail.
Moving the White point left (inward) emphasizes highlights and makes the image lighter. Normally you want to move the White point. The White Point determines level 255. Therefore values to the right of the White point are white too, and can contain no detail.
And you can do both in a balanced way to enhance the total range. This does not imply that you must always move both points, one may already be OK. The idea is that you see it all here, and then you know. You can experiment if you don't see the best choice immediately.
The biggest mistake is to NOT experiment. Be more daring and extreme than you think right. You may not like it, you may put it back, but at least you will have seen it (and you may like it!).
The scanner software will show the real time result of this adjustment, before you scan it. See its Before and After images above? It couldn't be any simpler, once you realize what you're trying to do. Simply experiment, and set what looks best. If you like it, then it's correct, at least for your purposes.
New scanned image with the Black and White points set.