The heat generated by a star pushes the atmosphere of the star out. As the star runs out of fuel the atmosphere collapses back on the star's core. If the star has a mass below the Chandrasekhar limit this collapse is limited by electron degeneracy pressure, which results in a stable white dwarf. If the star has a mass above the Chandrasekhar limit it has sufficient gravity to collapse past the white dwarf stage and become a neutron star or black hole.
The Chandrasekhar limit arises from taking account of the effects of special relativity in considering the behaviour of the electrons providing the degeneracy pressure supporting the white dwarf. In the classical approximation a white dwarf may be arbitrarily massive with its volume inversely proportional to its mass. In the relativistic calculation the typical energies to which degeneracy pressure forces the electrons in a massive white dwarf are non-negligible relative to their rest masses and a limiting mass emerges for a self-gravitating, spherically symmetric body supported by degeneracy pressure.
If a white dwarf in a binary system with a giant star accretes enough material to exceed the Chandrasekhar limit, the star collapses and becomes a type I supernova.
The limit was calculated by the Indian physicist Subrahmanyan Chandrasekhar.