That's called screentone. The idea is that it's borderline impossible to get a uniform gray that will be reproduced well by a printer if you shade the gray in by hand. Keep in mind that "gray" on a standard printer is actually just "small black dots with some white space" - which is not what a human with a pencil or an ink brush will produce.
Screentones, in their most basic form, are preprinted sheets of various shades of gray that can be cut and pasted onto a black-and-white drawing to impart some "color". As you can see, they are printer-friendly, since they consist of black dots on a white backdrop. Also, aside from the fact that they print better, it's just easier to cut-and-paste screentones than to draw stuff in by hand.
More elaborate screentones exist for other kinds of non-uniform textures, such as:
I would assume that professional manga artists and amateurs both use screentones for any serious work they do, though I imagine pros probably have access to (and make use of) a wider variety of screentones, being professionals and all.