I don't understand it, but I will say this: The way Zhang did it was, he first came to a state of high-to-complete understanding of all the previous papers that were going in this direction and/or provided useful tools (and this includes a LOT of different advanced number-theory techniques), then he realized that you could connect this to that, modify that, etc, to prove what he wanted. So he's very much standing on the shoulders of giants (not to minimize Zhang's accomplishment). And indeed, on Number Theory these days is getting eaten alive by a lot of powerful techniques that have been developed, and which are very technical, advanced, intricate, with about 20 different successive improvements piled on top of the first invention. E.g. "circle method," "kloostermania," "sieve methods," "L-function techniques," "Deligne's proven version of the RH" etc. Those things have grown into huge monsters. So the days when somebody who knows little can just solve "simple" easily-stated number-theory problems like twin primes, seem largely gone. Now, you need to spend mucho years learning all the previous machines, which are getting indispensable. Which all is rather frustrating to those of us who haven't. I mainly haven't. However, an exception to that trend was the discovery of the AKS primality test, which even I could understand. But it seems likely that the techniques Zhang has can get repurposed to prove a ton of other stuff, so there is motivation...