While socialism comes in many forms, one classic form involves ownership of the means of production by the workers. In the classic capitalist model, the means of production are not owned by the workers but rather by the capitalists.
This form of socialism began creeping into the United States with the advent of the stock market. In theory, workers could buy stock in the companies they worked for, thus becoming part of the owning class. This blurs the line between worker and owner, just as it starts to blur the line between socialism and capitalism.
Obviously, there is a considerable difference between a full socialist system and one in which workers can buy stocks in companies they work for. After all, owning a few shares of a company is rather different than being an owner in the classic sense.
While socialism is often presented as a great evil in the United States, the idea of a worker owning a business is held out as a great good. A small business in which the employees are also owners can be seen as a socialist enterprise, yet is something praised by conservatives who are against socialism.
Interestingly, the idea of workers having meaningful ownership seems to be consistent with (or perhaps even required by) democracy. In a democracy, each citizen is part of the nation and has a say in how things will go (at the very least, each citizen can vote). In contrast, the classic business model is completely undemocratic: the owner is like a king or feudal lord. He rules from on high and the employees serve at his discretion and usually do not have any meaningful say in the decision making. In contrast, worker owned businesses would seem to be democratic: business of the people, by the people and for the people.
Of course, it might be argued that the conditions in business are such that a democracy would be ineffective or inappropriate. After all, a business has to make quick decisions and voting would slow things down to much. Also, effective business choices require people who know the big picture and can make the tough choices that are needed for the business to succeed. Allowing the employees to get involved would interfere with this. Also, the employees would tend to vote for things like shorter hours, better working conditions, better pay, maternity leave, and better safety. These would cut into profits for the people who really matter, the top executives.
Interestingly, these same sort of arguments can (and have) been made against democratic forms of government. Likewise, arguments for democracy can be modified slightly to serve as arguments for worker ownership and control of business.