It is part of a hymn text.

Blest be the tie that binds
Our hearts in Christian love
The fellowship of kindred hearts
Is like to that above.

(That is from memory. You could probably Google it.) So, the hymn celebrates love among Christian. In the context in which you're seeing it, however, it is probably a reference to the marriage bond.

And what about the line in the Johnny Cash song "I Walk The Line":

I keep my eyes wide open all the time... I keep the ends out in THE TIE THAT BINDS... Because you're mine, I walk the line...

I just don't get it...

@TTB: There isn't necessarily a single meaning that's easy to paraphrase or translate. That's part of what makes songs and poems good, leaving some space for interpretation.

But 'keep the ends out' seems to suggest that the singer is holding out two ends of a rope or line, hoping that someone will take them and tie him to her. And he's looking not just for any romantic/sexual connection, but for 'the tie that binds': for real love, a lasting tie, not the casual hookups that once tempted him. (Since 'walking the line' probably means staying on the straight and narrow -- another originally biblical image BTW -- not going astray.)

Maybe he's even looking for 'the fellowship of kindred minds' (@S Johnson: good job, all you missed was the rhyme) -- a spiritual connection, a soulmate. And from what we know of Johnny Cash's story, probably also a relationship between Christians, as in the hymn.

Und wie wäre es dann zu übersetzen?