This is very difficult to translate, because the cultural connotations are so different. Literally, 緣 means hem, the hem on a garment, which doesn’t help a lot. BTW, it is pronounced yüán.
緣 is a concept that came to China with Buddhism. I believe that it is called paticca in Sanskrit. Anyway, the idea is that you come into somebody’s reach, into their life, for some attraction that you (both) have nurtured in the past. It could be good or bad, or very weak.
Let me give you three examples: I am trying to make this as simple as possible. This discussion could go on for a long time, but let’s keep it short. The first example, say five lifetimes ago, A was a rabbit and got stuck in a hole that it couldn’t get out of. B took pity on it and released it, saving A’s life. So in this lifetime, A feels very protective of B, or maybe just does something that helps B a lot. (Again, let me emphasize that this is very complex, I am stripping it down)
The second oversimplified example, A was down in that hole when C walked by, laughed at the stupid rabbit, and maybe kicked some dirt on it. In this lifetime, A will not like C and maybe do something to make C uncomfortable.
The third oversimplified example: there are over seven billion people on this beautiful, overloaded planet. Tuesday I was in the city and took the subway; a man sat next to me, a lot of people were in the car. Of all seven billion people in the world, this man sat next to me because in some situation we had a similar situation. If you ask me who he was, where he lives, what he does, I have no idea, because although our 緣 exists, it is very weak. In a similar situation, all of us who share questions and answers on Quora have some sort of 緣.
Again, I could go on and on, but I hope this gives you an idea. It is a central concept of Chinese thought, and quite common. Let’s say that stranger sitting next to me fell and his stuff scattered all over the place, I helped him gather things, and he thanked me. I could say, 都是有緣人 we all have 緣.
I’m sure you’ve met people who you immediately cotton to: 我們很有緣: we have plenty of yuan, 我們很投緣 (literally) we throw hems (ha). But then there are people who just rub you the wrong way, 不投緣, it’s also a matter of yuan. Or say two people fall in love, have a close relationship, but after a period of time drift apart and see each other no more: 緣盡了 the yuan is all used up.
You can also see that there’s more to Johnny Depp and Amber Heard than on the surface, and their recent behavior ensures that they will be tied together for a long, long time.
You should see why it is so difficult to translate it. The Buddhist television channel, 大愛電視, translates it affinity and lets it go at that. That is just about as good as you can do in English.