生き甲斐
いきがい · ikigai · JLPT N1 · noun
something one lives for
生き (live) + 甲斐 (worth, payoff) = the payoff of living, what makes life worthwhile
甲斐 means worth or payoff, as in 努力の甲斐がある (the effort pays off). So 生き甲斐 is the payoff you get from living: the thing that makes your life feel worth it.
生 — sprout 屮 above earth 土
Originally a pictograph showing a young plant sprouting from the ground, with 屮 (a sprout) above 土 (earth). The core meaning is 'to be born, to grow, to live,' which extends to 'raw, unripe, unfamiliar.' The modern form has simplified the sprout shape but preserves the image of new growth emerging from soil.
甲 — pictograph of a seed sprout's hard shell
甲 originally pictured the cracked shell of a seed as it sprouts, or the hard carapace/armor of a turtle or insect. From this came meanings like 'shell,' 'armor,' and 'helmet.' It was later borrowed as the first of the ten Heavenly Stems, giving it the sense of 'first' or 'A-grade.'