A bound nucleus has less mass than the sum of its separated protons and neutrons. If a nucleus contains $Z$ protons and $N$ neutrons, its mass defect is $$\Delta m=Zm_p+Nm_n-M_{\rm nucleus}.$$ The corresponding binding energy is $$B=\Delta mc^2.$$ This is the energy required to separate the nucleus completely into free nucleons, or equivalently the energy released when those nucleons bind.

The binding energy per nucleon $$\frac{B}{A}$$ is a useful measure of nuclear stability. It rises rapidly for light nuclei, reaches a broad maximum near iron and nickel, then decreases gradually for very heavy nuclei.

This curve explains why both fusion and fission can release energy. Combining light nuclei can move the products toward larger binding energy per nucleon; splitting very heavy nuclei can do the same from the opposite side.

Suppose a reaction reduces total rest mass by $0.001,\mathrm u$. Using $$1,\mathrm u,c^2\approx931.5,\mathrm{MeV},$$ the released energy is about $$0.001\times931.5\approx0.932,\mathrm{MeV}.$$ Tiny mass changes therefore correspond to nuclear-scale energies far larger than typical chemical bond energies.

Binding energy is not extra material 'stored inside' a nucleus. It is the difference in total energy between bound and separated configurations, expressed as an equivalent rest-mass difference.