Binary stars can evolve to become novae and supernovae because slight differences in mass can mean large differences in main-sequence lifetimes.

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Binary stars are two stars that orbit a common center of mass. If one star in a binary system is slightly more massive than the other, it will evolve faster and exhaust its fuel first. As a result, the more massive star will evolve into a red giant or supergiant first, and its companion star will continue to evolve as a main-sequence star. If the red giant or supergiant star is close enough to its companion, it can begin transferring matter onto the other star. This can lead to a buildup of hydrogen gas on the surface of the companion star, which can eventually trigger a runaway fusion reaction and result in a nova explosion. 
Alternatively, if the more massive star undergoes a supernova explosion, it can leave behind a neutron star or black hole, which in turn can interact with its companion and lead to additional supernova explosions or other forms of intense stellar activity. Thus, even small differences in mass between binary stars can have significant impacts on their evolution and eventual fate.

Binary Stars Can Evolve to Become Novae and Supernovae Because