we knew that for some atoms are more stable that others. like He, Ne, Ar, etc, which are belonged to noble gas. the reason for they are non-reactive is, there outer most electron shell is filled out.
similar things happened in nuclei. in the shell model of nuclei, protons and neutrons just like the electrons in atom. if the outer most shell of proton or neutron is filled out, the nuclei is very stable. and we called this number of proton or neutron be MAGIC NUMBER.
the first magic number is 2. nuclei with 2 protons is more stable then others. However, if only have 2 protons, with out neutron, it is very unstable because of coulomb force. and 2 neutron also unstable, if without a proton. the only stable 2 nucleons state is deuteron. If there are 2 protons and 2 neutrons, we called this double magic number, and this nuclei, which is He is very very stable.
the list of magic number is 2, 8, 20, 28, 50, 82, 126 in theory prediction.
however, when the nuclei become heavier and heavier, the stability of nuclei in the magic number lost. to understand this. we have to know that the magic number is come from the large spin-orbital coupling term in the Hamiltonian of the nuclei. and recent research suggest that, the spin-orbital coupling may change by the number of nucleons.