noun
worth talking to; rewarding to talk with
Refers to the value or satisfaction gained from talking with someone. Often used in expressions like 話し甲斐がある (it's worth talking to them) or 話し甲斐のない (not worth talking to).
彼は話し甲斐のある人だ。
He is someone worth talking to.
あの人と話しても話し甲斐がない。
There's no point in talking to that person.
やり甲斐 refers to the worth or reward of doing something, while 話し甲斐 specifically refers to the worth of talking with someone.
Compound of 話し (stem of 話す, 'to talk') and 甲斐 (がい, 'worth, effect').