A nuke works on principles of nuclear fission. Basically you have a radioactive substance like uranium whose atoms have relatively large nucleus. So when you hit the nucleus with a neutron, the nucleus splits into two smaller nuclei and also releases two or three more neutrons are released along with some energy. These neutrons further hit other nucleus and they release energy and neutrons and this starts a chain reaction leading to sudden outburst of energy.
In a nuclear weapon, the same principle applies. It has Uranium inside it and an inbuilt mechanism leads to release of neutron which hits uranium and the chain reaction (fission) starts leading to a big explosion.
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