Funds of funds are mutual funds that invest in other mutual funds. That may sound redundant, but it's true.
Just as a regular mutual fund offers the skills of a professional manager who assembles a portfolio of stocks or other securities, the manager of a fund of funds will select a portfolio of funds, managed by other managers.
If you have only a small amount to invest each month, a fund of funds allows you access to more funds than you might be able to afford on your own. It also allows investors to avoid the recordkeeping and paperwork that comes with owning an assortment of funds.
So what's the catch? Expenses, mostly. The fund of funds structure creates a double layer of costs. First, there are the expenses associated with running the fund of funds itself—management fees, administrative costs, etc. Second, there are the costs associated with the underlying funds—the same sorts of management fees, administrative costs, and so on. A fund of funds may report an expense ratio of just 1%, but keep in mind that you're still paying the expense ratios on each and every fund that the fund of funds owns.
Some fine funds of funds eliminate the double-fee problem. Families such as T. Rowe Price and Vanguard offer funds of funds that invest only in their own funds. The families then waive the cost of the funds of funds—their reported expense ratios are 0%—and you only pay the costs of the underlying funds. Obviously, these funds are a much cheaper option.