I define irrational as illogical. I can't really define it without just reverting to using synonyms. The presence of feelings or emotions or convictions which run contrary to a)survival b)the advancement of your position in life.
...in other words, doing things differently than say, a Vulcan (you get the point) would.
Art is, in objective terms, useless. As are most emotions such as love, fun, justice, freedom. Pondering existential questions s useless, since there is no answer, and even if there was, it wouldn't really benefit you (except mentally) to know it. Many, maybe most, of the things which humans do are well beyond the scope of rational self-preservation, and sometimes directly contrary to it. Dying for a loved one, how is that rational? Having hope despite a hopeless situation, how is that rational? Craving freedom and justice for their own sake, how is that rational? Displaying compassopn even when it benefits you nothing, how is that rational?