She is referring to Hijiri actually, its a religious thing, almost like with nuns. Hijiri is of higher status in the temple, so Ichirin and the others may at times refer to her as the 'big sister.'
Traditional belief in hospitality, I'd imagine. It's sort of a universal thing that guests are to be well-treated.
Who's the one that usually takes care of the cooking at your home?Hijiri.Let's eat.Oh? Can I?Set Meal AIf you don't mind, how about coming with us to our place for a bit, Kyouko?Big sis.Umm... Where are the side dishes?Huh? There aren't any.