Socialism is a word that often gets used incorrectly. Socialism advocates for public or collective control over the means of production, distribution, and exchange. Put simply the government owns the factories, farms and shops. As a form of government, socialism is now very rare. Now days socialism is used to describe any policy that advocates for the redistribution of wealth or involves government participation in the economy, such as universal healthcare or social welfare programs. In the USA for example any politician who says there should be a universal health care programme like the one we have in NZ is branded a socialist.
Far more common are social democracies, such as Sweden and Denmark which have private ownership of most of the production [i.e free market] but also use state intervention to ensure a fairer distribution and prevent market excesses.