In The Order of the Phoenix, Voldemort uses Avada Kedavra on Harry, but Dumbledore clearly deflects it.
But in The Goblet of Fire, Moody mentions that there is no way to fend off that particular Curse.
So how did Dumbledore do it?
I believe Dumbledore made the statues in the ministry come to life to take the hit for him/block the hit. He didn't use any counter-curse or counter-jinx directly on the Avada Kedevra spell
But the headless golden statue of the wizard in the fountain had sprung alive, leaping from its plinth to land with a crash on the floor between Harry and Voldemort. The spell merely glanced off its chest as the statue flung out its arms to protect Harry. "What -?" cried Voldemort, staring around. And then he breathed, "Dumbledore!" -OOTP
Voldemort uses the killing curse several times in the Battle at the Ministry.
The first time Voldemort aimed it at Harry and Dumbledore animated the golden wizard statue: "The spell merely glanced off its chest as the statue flung out its arms, protecting Harry" (pg 813 of Scholastic paperback).
Next time: "Voldemort raised his wand and sent another jet of green light at Dumbledore, who turned and was gone in a whirling of his cloak;" (also pg 813)
Third time: "[Voldemort] sent another Killing Curse at Dumbledore but missed..." (pg 813)
Next: "Another jet of green light flew from behind the silver shield. This time it was the one-armed centaur, galloping in front of Dumbledore, that took the blast..." (pg 813)
Finally: "But even as he [Harry] shouted, one more jet of green light had flown at Dumbledore from Voldemort's wand...Fawkes swooped down in front of Dumbledore, opened his beak wide, and swallowed the jet of green light whole. (pg 815)
Voldemort's killing curses either missed, hit non-living objects, or was swallowed by Fawkes, who "died" in his own way, falling "to the floor, small, wrinkled, and flightless."
Dumbledore didn't actually block the Avada Kadavra as much as avoid it or was protected by things and beings that can't be killed.
As several others have mentioned, during the battle at the ministry Dumbledore used something like an animation charm to make the statues of the Fountain of Magical Brethren protect Harry from the curse, from reading the books I believe that an animated object is given a facsimile of life so the curse killed the statue, moreover, any spell, even the Avada Kadavra can be blocked by a physical object of a large enough size and density, so when Moody mentions it being unblockable he's referring to all magical means of protection such as the Protego shield charm or a runic protection or some such magic
I do believe the topic poster is referring to the movie, in which Voldemort casts Avada Kedavra and Dumbledore creates a spell-lock with it, kinda like the graveyard scene. Also, in the movie for Harry Potter 7, Part 2, Battle of Hogwarts, Voldemort is show Avada Kedavra'ing the heck out of Harry, who is casually deflecting them magically, although this can be attributed to the imbalance of the Elder Wand belonging to Harry and Harry using a wand he actually did own, or to Voldemort's life protecting Harry's.
The movies do seem to kind of not care about the books' rules of magic at many points, and the OoTP fight scene and Battle of Hogwarts are just two of many examples of this. At this point, I would assert that the book's version of events are what "actually took place".
Dumbledore didn't block it, he just cast it away meaning he curved it and it hit the wall anyways and we just can't Avada Kadavra curse by Protego or any other attacking spell.
Like Harry used Expelliarmus to block Avada Kadavra, he didn't really block it, what he did was like two lasers attacking each other and making a circle of power, one more example take two pipes of water direct them to each other then turn on the water the one with more pressure and water will win