Coarse can mean rough to the touch or vulgar. It's good to have coarse sand paper, but not good to have coarse manners.
Do you lick your dinner plate, wipe your nose on your sleeve, and generally behave like an oaf? No, of course not. You're the kind of person who reads online dictionaries. But if you did do any of things, you'd be coarse — that is, unrefined, boorish, and downright vulgar. Coarse can apply to a wide variety of things other than behavior. If something is of poor quality, cheap and inferior, it's considered coarse.