Reason For Living
Something Worth Living For
noun
You know that 甲斐 is "effect" or "worth." So, the "worth for being alive" is your reason for living. It gives life worth. It's your reason for living.
いきがい
The readings come from 甲斐 and 生き, so if you know those you may have a reason for living, or at least a reason for doing your kanji study.
ロッククライミングは私の生き甲斐です。
Rock climbing is what I live for.