The following site has a good explanation http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/961130b1.html I hope it is helpfull.

Nemesis is a hypothetical red dwarf star or brown dwarf, orbiting the Sun at a distance of about 50,000 to 100,000 AU, somewhat beyond the Oort cloud. The existence of this star was postulated in an attempt to explain an inferred periodicity in the rate of biological extinction in the geological record. http://en.wikipedia.org/wiki/Nemesis_(star) - Like a thorn in the side of mainstream researchers, Muller's Nemesis theory -- that our Sun has a companion star responsible for recurring episodes of wholesale death and destruction here on Earth -- seems to reemerge periodically like microbes after a mass extinction. It's a theory that has many detractors. And it's a theory that has been beaten down and left for dead in the minds of most scientists. Yet it is a theory that just won't die. Nemesis is cautiously supported by a handful of scientists, who often sound like ringside rooters eager for a victory but thankful they don't have to put the gloves on. Muller meanwhile acknowledges the possibility that the whole idea could turn out to be wrong, but he is nonetheless confident that Nemesis will be found within 10 years. "Give me a million dollars and I'll find it," Muller said in a recent telephone interview. Brave words for a bold theory that if proven true would shake up everything we know about the formation and evolution of our solar system. http://www.space.com/scienceastronomy/solarsystem/nemesis_010320-1.html