Mindless things are done without any care or thought. If the kid sitting next to you in class won't stop the mindless tapping of his pencil against his desk, you'll have a hard time focusing on your vocabulary quiz.
If something's careless or lacks reason, you can describe it as mindless, like the casual, mindless violence on a TV show. A mindless task is one that you can do without even thinking about it, like sweeping the sidewalk or stuffing fliers into envelopes. Mindless comes from the Old English myndleas, "foolish or senseless."