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 limit was calculated by the Indian physicist Subrahmanyan Chandrasekhar.