tl;dr - Any changes put in place by Convergence were largely not used by writers, and will be subsumed and overridden by DC Rebirth.
This will likely be a somewhat confusing answer, I shall try to remain low-detail.
The big new point from Convergence was the idea that continuity in the books could be more malleable from an editorial sense. Events from pre-52 eras were potentially useable. Dan Didio tried to explain it in this interview at Newsarama.
The Lois and Clark title features the Pre-52 Superman and Lois, the ones that were married. They were saved from the cataclysm of Flashpoint by Telos, who placed them on his collection planet, the events of which were covered in Convergence. We now learn that he, Lois, and their son (we shall tastefully leave the Larry Niven-esque discussions about that to the side) survived and made it to what is the prime DC-Earth, on which the current events of DC's titles were occurring. He is living incognito, allowing the Superman of this Earth to be Superman, only engaging in secret rescues.
Events in Superman and Justice League, and then filled in by Rebirth, will result in...let's say, a position change for this pre-52 Superman.
The Rebirth version of the DCU will have some big changes for many characters, most of which involve returning to a earlier, more "positive" take on them. Ted Kord is back, and is working with Jaime Reyes, the new Blue Beetle. Ryan Choi is alive, and Ray Palmer is back in the role of The Atom, and not the mad scientist of S.H.A.D.E. The Legion of Super-Heroes appears to be back in play.
it's not quite a complete reboot, but enough changes are in play to make much of the recent history of many characters, both pre-Convergence and pst-new 52 up for some rewriting.