Why nuclear fusion deliver energy instead of taking? 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!
 A: Good question. To think of it in that way can be very confusing. Every atom wants to reach the least energetic state it possibly can. This is what happens in fission, as you explain, and the uranium nucleus gives out energy after it splits into other nuclei, as those daughter nuclei have lost energy in order to reach that state, lost the energy which we use.
Why do they lose energy though? This is where binding energy comes in. Binding energy is defined as the energy required to split a given nucleus into it's individual protons and neutrons. Rephrased, it is the energy released when protons or neutrons come together to form an nucleus.
Now the binding energy is not what determines the stability, but the binding energy per nucleon (protons and neutrons are collectively called nucleons, as they constitute the nucleus) that determines it. For example, if one man has a 100 dollars, and a family of 10 has 500 dollars, the family has more money collectively, however, individualy, the man has more money.
In the same way, it is the binding energy per nucleon , that determines the stability. The graph of binding energy per nucleon vs the elements is given-

You can see that iron, has the highest binding energy, which makes it the most stable element. Now every atom wants to attain this stability that iron has. Uranium, on the right side of the graph, should split in order to come closer to the binding energy per nucleon value that iron has, whereas light elements like hydrogen need to fuse in order to gain iron's stability.
You can see that hydrogen is way below iron in the graph, which is also why fusion releases a lot more energy than fission. 
I hope you understood, have a great day!
A: The answer comes down to the relative strength and mechanism of the strong nuclear force and the electromagnetic force.
Up to a certain point, the mass-energy of a larger nucleus is lower than the separate smaller nuclei that fuse to it. For example, two hydrogen nuclei + two neutrons separate from each other weigh more than a helium nucleus. Since the lower energy state is favorable, the four particles will fuse if they are brought together and release the extra energy. Of course the electromagnetic repulsion must be overcome for that to happen, which is why fusion requires high temperature to get started, but once conditions exists, fusion is favorable because the strong force overcomes the electromagnetic force to bind the nucleons. This process occurs spontaneously up to iron, after which it is no longer energetically favorable to fuse - larger nuclei are the product of endothermic, rather than exothermic, fusion reactions generally only occurring during supernovae and similar catastrophic events.
In a very large nucleus like Uranium however, there are a large number of protons, which repel electromagnetically. But unlike the smaller nuclei, the strong force cannot reliably bind the nucleus due to its short range. Protons on opposite sides of the nucleus experience electromagnetic repulsion on par with the nuclear binding forces and sometimes will break off. In this case the fission is energetically favorable, bringing the nuclei closer to lower energy state of an iron atom, where the nucleus is small enough to be kept together be the nuclear forces.
So there's a saddle point at iron where the energy is most favorable, so fusing up from smaller nuclei releases energy due to strong force binding and fissing (is that a word?) down to it is favorable due to electromagnetic repulsion. 
