This is the title of Book Two and also a phrase we hear twice inside the text. The first occurrence comes at the end of Book One, when Charles is out to dinner with Cordelia at the Ritz:
"D'you know what Papa said when he became a Catholic? […] He said […]: 'You have brought back my family to the faith of their ancestors.' […] The family haven't been very constant [in regards to religion], have they? There's him gone and Sebastian gone and Julia gone. But God won't let them go for long, you know. I wonder if you remember the story Mummy read us the evening Sebastian first got drunk – I mean the bad evening. Father Brown said something like 'I caught him' (the thief) 'with an unseen hook and an invisible line which is long enough to let him wander to the ends of the world and still to bring him back with a twitch upon the thread.'"
Cordelia paints the image of God with essentially a fishing line tied to every Catholic. A given Catholic – like Julia, for example – might wander away from God, but God can pull on the thread (or give it a "twitch" in this case) and yank him right back at any time.
As the titles of Book One and Two of Brideshead suggest, Book One is the wandering away part and Book Two is when everyone gets yanked bank by the twitch. Sebastian wandered all the way to Northern Africa, but ended up where? At a monastery. Julia abandoned God and the sanctity of her marriage, but returns to her faith at the end of the novel. Lord Marchmain was never much for religion, but accepts the Last Sacrament on his death bed. Notice what Charles says when Lord Marchmain refuses the priest for the first time: "I felt triumphant. I had been right, everyone else had been wrong, truth had prevailed; the thread that I had felt hanging over Julia and me ever since that evening at the fountain had been averted, perhaps dispelled for ever." And notice Julia’s very reason for breaking up with Charles is right in line with Cordelia’s thread metaphor: "The worse I am, the more I need God," she says. "I can't shut myself out from His mercy."
Most surprising of all is the twitch upon the thread which brings Charles to Catholicism. But we talk about that in "What’s Up With the Ending?"