If it's your turn to bring in the coffee and donuts for your early morning meeting, and you forget, then your co-workers can say that you were remiss in fulfilling your responsibility to keep them awake with sugar and caffeine. Don't expect to get much done at your meeting.
The adjective remiss is often used in the phrase "remiss in one's duty." The principal was remiss in her duty to tell parents about the incident at school. After the parents heard about it from their kids, the principal received several angry phone calls wondering why the school had been locked down for loose farm animals.