An open-end investment company (the most common type of mutual fund) that invests in other open-end investment companies.
The most commonly noted benefit to this is reduced risk, because your portfolio is spread over a very large number of investments. Some fund of funds will also balance your funds for you; for example, some people advise that 20 years or so before retirement you should invest primarily in stocks, and as you approach retirement you progressively shift over to safer investments, such as bonds. Funds of funds will often do this automatically for you, switching some of your investments from mutual funds focusing on stocks to others focusing on bonds as time progresses.
A disadvantage to this type of setup is that any time you invest in a mutual fund you pay a small commission to the investment company running the fund. A fund of funds adds on one more level of commissions that comes out of your pocket.
Funds of funds were very popular in the 1960s; since then they have decreased in popularity, sometimes being seen as more gimmicky than useful -- but they're still around, and offered by some quite respectable investment companies.