When an atom of a radioactive element is hit by a neutron, it can split into two smaller atoms, and shoot off more neutrons, which can then hit other atoms. Usually, in nature, there aren't enough radioactive atoms together in one place for this to keep happening; the neutrons go flying off and hit non-radioactive matter.
But if you have a high enough density of radioactive atoms (a critical mass), what happens is that one atom decays, which spits out neutrons that hits others and makes them decay, on and on and on in a cascade. Each of these reactions releases energy, and if you've got enough, it'll explode.
Now, if you just stick one 'sub-critical' lump of plutonium next to another 'sub-critical' lump, together they can 'go critical,' and you'll kill everyone nearby with radiation. What most nuclear weapons do is have a sub-critical quantity of uranium or plutonium, then use external explosives to compress that mass into a smaller volume. Like if you take a marshmallow and squeeze it into a tiny ball, only you've got something already quite dense and you're compacting it more.
This sets off a massive chain reaction, which explodes.
(Modern nuclear weapons use a fission bomb like this to trigger a fusion reaction, but I understand that less well.)
Now, this is a movie, and they're talking about some sort of fusion energy device. Their device looks to be WAY smaller than any fusion reactor I've ever heard about, outside of maybe Battletech. I assume it was designed with Hollywood science (i.e., bullsh*t). If I followed the exposition correctly, the reactor had some sort of core that could be modified into a bomb, that could be triggered at any moment. Fair enough.
Then, for a bit of (in my opinion) unnecessary extra tension, they tossed in the fact that, if removed from its housing, this bomb becomes unstable . . . but a very precise sort of unstable, so you can predict when it will go off, to the second, 5 months from now.
Again, I think it would have made more sense if they'd just left that out. Instead, have the bomb have both an immediate trigger and a countdown. The villains could be waiting to watch Gotham fall apart, and then will cap things off by blowing up the city as they get away. When Batman gets back, he could have led the effort to free the city, and things could have gone exactly the same.
Talia, like, has the control device and presses button 1 to prime the bomb, which starts the countdown. Then when she pressed button 2 to actually set it off, the jammer stops that. Realizing Batman and company are going to try to disarm the bomb, she decides to martyr herself for the cause, and stays in the city so she can keep control of the bomb until it explodes.
But that's just a small nitpick. Overall I loved the movie.
