This is an area being actively debated. Active fund managers justify their fees by claiming to "beat the market." For investors, of course, given the wide availability of low fee passive index funds, unless a fund manager can show consist returns (after fees) higher than index funds, there is no reason to invest in an actively managed fund. Historically, in fact, actively managed funds do significantly worse than the market.
Here we run into somewhat of a conflict of interest. If a manager is acting as a fiduciary, the best interest of her client would be low-fee index tracking funds. Market timing over the long term actually underperforms absolutely random picks. Of course, holding index funds earns the manager fewer fees than churning individual equities.
A fund manager should, however, create a portfolio balanced globally, including developed, emerging, and frontier markets. As these often follow different patterns, this minimizes overall risk. Also, in addition to stocks and bonds, a manager can also invest in other products such as infrastructure financing, real estate investment trusts, and private equity.
Perhaps the major challenge a fund manager faces is that there is no way to "beat" a "perfect market" in which everyone has full access to identical information, as prices would rise and fall in direct proportion to actual value.
Another major challenge now is the increasing automation of trading and the speed at which it occurs. For high-speed trading, the actual time it takes a message to travel across fiber optic cable can affect the success of some trading strategies. The computing power and even location of the computers that make trades can be key issues.