A public option would require private insurers to compete for business, which would likely drive down costs, provide people with more choices in the market place, improve quality and access, and prevent some of the worst abuses of the private market.
See this article from the Economic Policy Institute:
Many leading policy makers, including President Obama and Senate Finance Committee Chairman Max Baucus, have argued that the creation of a public insurance plan is a necessary part of comprehensive U.S. health care reform. This public insurance plan would compete directly with private insurers within a new national insurance exchange. Americans in the exchange would be able to choose between an array of private plans, or the new public plan, within a marketplace that ensured a common set of rules for all insurers. Some have argued that a well-designed exchange with sufficient regulations would make a public plan option unnecessary. This is unlikely to be the case as a public plan provides crucial benefits to the U.S. health care system even within a well-designed exchange.