1. fate; destiny
考えてみれば、実に不思議な因縁と言わねばなりません。Come to think of it, I have to say it's a truly strange twist of fate.
2. connection; tie; bond; origin
あのお二人は、何か因縁があるのですか?Is there some history between those two?
3. pretext; justification
4. hetu and prataya (direct causes and indirect conditions, which underlie the actions of all things)