If hair or grass is close-cropped, it has been cut very short, close to the skin or to the earth. Close here means 'near' — the cut sits near the surface. For hair, think of a buzz cut or a very short army style, not just 'a bit short'. For grass, a lawn cut almost down to the dirt. It is a describing word, a little more 'written' than simply saying very short. You mainly meet it with hair and grass; people do not usually say a close-cropped hedge in everyday talk, though the picture would still make sense.