White dwarf stars are the end products of the stellar evolution of low to medium mass stars like our Sun. They are extremely dense objects (1 teaspoon of white dwarf material would weigh several tonnes!) and are supported against further gravitational collapse by electron degeneracy pressure.
The Chandrasekhar Limit of 1.4 solar masses, is the theoretical maximum mass a white dwarf star can have and still remain a white dwarf (though this limit does vary slightly depending on the metallicity). Above this mass, electron degeneracy pressure is not enough to prevent gravity from collapsing the star further into a neutron star or black hole.
The limit is named after the Nobel laureate Subrahmanyan Chandrasekhar, who first proposed the idea in 1931.