Here is an excellent editorial that was in the San Jose Mercury News by Stanford professor Dan Edelstein further explaining why it is so wrong for Republicans to be using this term. He also provides a definition of socialism:
Socialism, as it was theorized in the 19th century and put into practice by the Soviets, was the nationalization of everything — all the "means of production": banks, yes, but also industries, farms, even private property. It was an economic philosophy that explicitly rejected the market economy and capitalism, seeking instead to have the state direct economic growth through "five-year plans" and other centralized measures.
This is not at all what is happening in this country, and it is maddening that the media is propagating this myth with headlines like Newsweek's "We Are All Socialists Now". Republicans are using the term as a code word for Communism, and it absolutely laughable. However, the media is not setting anyone straight with the facts and history of the term.
Government spending is not socialism. A progressive tax system where the marginal tax rate increases as income increases is not socialism. Helping the nation's needy is not socialism. Developing a health care system that attempts to provide affordable health care for those who cannot currently afford health insurance or get it provided by their employer is not socialism. Providing services through government is not socialism. Government funding of scientific research is not socialism.
Check out the article from an expert on the history of socialism.