First, neutrons hitting the nucleus of most atoms will either do very little or will actually use up energy. Only "fissile" materials will generate more energy, such as some forms of uranium and plutonium.

When an explosive chain reaction happens, two things cause it to end quickly:

1. The fissile atom's nucleus changes when it releases energy. The atom becomes a different element. The elements that result are non-fissile. As a result, the fissile material is used up, leaving no fuel for the chain reaction.
2. In order to have enough neutrons hit other atoms in the fissile core, that core has to be pretty dense. When the explosion happens, the fissile material spreads out in a cloud of superhot plasma. This plasma is not dense enough to maintain fission.