The biggest advantage is the instant diversification a fund can give you. Many people don't have enough money to buy a portfolio of stocks and bonds that is varied enough. Pooling your money with thousands of other investors solves that problem, ideally spreading your money across enough investments to reduce the risk of you being wiped out by any single bad bet.
Another advantage is that investing in mutual funds saves time. You've essentially hired a professional investor to monitor your portfolio's holdings and do his or her best to buy and sell at appropriate times. You don't have to spend your time poring through stock Web sites and company news in order to make those decisions yourself. (Of course, if you love doing that, then investing in individual stocks and bonds may be right for you.)