Well, it was some catch by Chris Lynn, an Australian cricketer. The catch was held on 25 Apr 2014 in IPL’s 7th edition. I am not sure it was the best in history as said in this quora post (and elsewhere) but surely one of the greats. Apparently Lynn showed his catching brilliance earlier as well.
So this Quora post discusses how did Lynn end up taking the catch as he had slipped just moments before the ball came towards him. And more importantly how he managed to avoid falling on the rope considering how close he was to it.
People have looked at ideas from Physics to explain how the catch was possible. I have zero knowhow of Physics (though know some bit of economics :-)) so no comments at all. But some interesting explanations.