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.
生き甲斐 is a noun so usually gets used and translated that way, like 仕事が生き甲斐 (work is a reason for living) or 生き甲斐が欲しい (want something worth living for).
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.