These are in a book I'm reading. I think they might be related to Buddhism. I can't find them in any dictionary I have at my disposal, internet or otherwise.
親鸞 is a Buddhist monk who lived in the early part of the Kamakura era (1192-1333). He is I believe to be the founder of the Jodo (Pure Land) sect of Buddhism. One of his students collected his teachings after his death in the tomb entitled 歎異抄.
業縁 is hard to explain. I found the explanation カルマの実施縁 In Buddhism, as I'm sure you're aware, there is the concept of cause and effect. There are two kinds of cause, broadly speaking: direct (因) and indirect (縁). So 業縁 is the indirect cause (of future suffering or pleasure) brought about by the process of Karma working, according to this explanation. Sorry, I know this isn't very good...