Both mutual funds and hedge funds are managed portfolios. This means that a manager (or a group of managers) picks securities that he or she feels will perform well and groups them into a single portfolio. Portions of the fund are then sold to investors who can participate in the gains/losses of the holdings. The main advantage to investors is that they get instant diversification and professional management of their money.
Risk and Reward
Hedge funds are managed much more aggressively than their mutual fund counterparts. They are able to take speculative positions in derivative securities such as options and have the ability to short sell stocks. This will typically increase the leverage – and thus the risk – of the fund. This also means that it's possible for hedge funds to make money when the market is falling. Mutual funds, on the other hand, are not permitted to take these highly leveraged positions and are typically safer as a result.
Another key difference between these two types of funds is their availability. Hedge funds are only available to a specific group of sophisticated investors with high net worth. The U.S. government deems them as "accredited investors", and the criteria for becoming one are lengthy and restrictive. This isn't the case for mutual funds, which are very easy to purchase with minimal amounts of money.