This question already has an answer here:
In nuclear physics, when you break eg. a nucleus of Uranium, some neutrons are liberated, and the original atom degrades to a lighter element. The energy that was used to keep these subatomic particles together is liberated (strong interaction), and a small part of the mass is converted to energy (E=MC^2) so you get a lot of energy with a small amount of atoms.
So why nuclear fusion (the opposite operation) could even liberate MUCH more energy? I would naively expect it to take a lot of energy, not liberate it.
I'm not a physician nor a student, just interested in physics, and this has always been a mystery to me.
EDIT: actually, both of your answers are great and cristal-clear. That makes perfect sense and is exactly what I was looking for. I wish I could accept both answers, but the one with the graphic was a bit more complete. But thank you two!