Someone indefatigable does not give up, and they do not seem to get tired of trying. It is a praise word, and a rather grand one. You might call a campaigner, a night-shift nurse, or a stubborn researcher indefatigable. Though actually, almost nobody says this at the dinner table. “Tireless” and “they never give up” are the everyday versions. Indefatigable sounds like a speech, a prize citation, or an old novel. It describes spirit more than muscle: you can be physically exhausted and still indefatigable in the work. The British navy even named a ship HMS Indefatigable — they meant it as a compliment. Do not use it for a person who is merely busy. Busy is a calendar. Indefatigable is a will that does not run out.