An index fund is a mutual fund or exchange-traded fund that tries to mimic the distribution of a major stock market index. Common examples are the Dow Jones, S&P 500 or NASDAQ. Basically, a Dow Jones fund would be invested in the very same list of stocks that the Dow Jones tracks at any given time.
Index funds provide several advantages. First, they offer immediate diversification in most instances, because they mimic a broad index. Second, because they just follow a set list, they are not actively managed, meaning there is far less fees for management and transactions. Third, because they mimic an overall stock market, they by nature perform as well as the general stock market in growth years.
While traditionally following broad stock markets, there are index funds targeted to more focused goals, like particular foreign markets or bond sectors. The 'set-it-and-forget-it' nature of index funds makes them good investment vehicles for those without a lot of personal experience in investing or the risk-averse.