How does splitting a heavy nucleus release so much energy, and how is that energy controlled?
Nuclear fission releases energy because the products are closer to the peak of the binding energy per nucleon curve (near Fe-56) than the original heavy nucleus. When uranium-235 absorbs a slow neutron, it becomes unstable and splits into two medium-mass daughter nuclei plus 2–3 fast neutrons — each of which can trigger further fissions. This chain reaction can be explosive (nuclear weapon) or controlled (nuclear reactor), depending entirely on whether the multiplication factor is kept at exactly one.
A nuclear reactor is fundamentally a heat exchanger with a fission chain reaction as its source. Control rods (boron or cadmium) absorb neutrons and are lowered to reduce reaction rate; a moderator (water or graphite) slows fast neutrons so they are more likely to be absorbed by U-235 (thermal neutrons are far more effective at inducing fission than fast ones); coolant carries heat away to drive steam turbines. The design has to ensure negative feedback — if temperature rises, the reaction rate should decrease, not accelerate.