Index funds are mutual funds which are designed to match the performance of a market index. As an example, a mutual fund may be intended to track the Russell 3000 Index. Such funds are usually passively managed, and as such, tend to capture the increases in the underlying index. These funds, however, are generally not protected against sharp declines in the value of the underlying index. Index funds typically charge lower management fees than ordinary mutual funds because their strategies are mostly dictated by the underlying index. As a result, portfolio turnover may be less frequent and transactions may even be automated to closely mirror the performance of the underlying index.
To expand upon Martin's answer, the ETF industry has continued to grow significantly due to many fund providers creating unique indexes to support their ETF products. There is now an ETF for nearly every broad based index from Wilshire, Dow Jones, S&P, and Russell. In addition, the fund providers are creating fundamental indexes that select stocks centered around rules based criteria such as sales, earnings, book value, cash flow and dividends.
As the ETF industry continues to evolve they will create and release new indexes for more niche company sectors, industries, and strategies. Ultimately some will be successful and others will fail, but it's up to the investor to decide if the index meets their goals for diversification and exposure to a specific asset class.
Index funds also trade on stock exchanges and are called, ETFs, exchange-traded funds and ETNs, exchange-traded notes. Both seek to replicate the movements of an index of a specific market and now include commodities as well as financial assets. ETNs have credit risk associated with them.
Some Index Funds are constrained by a set of rules that are held constant, regardless of market conditions. And recently, "enhanced" indexing that employs active money managers, has emerged.
An index fund is any vehicle that provides exposure to an index. The structure could be an Exchange Traded Fund, Exchange Traded Note, Mutual Fund, Closed End Fund, etc. Although, most commonly used vehicle is an Exchange Traded Fund. These are generally rules based and do not involve any manager subjectivity. The most common index fund is SPY, which provides exposure to the S&P500 Index.
These are generally considered passive investments, as they merely replicate an index at a low total cost and do not need to be actively managed. However, given that the markets have been sliced and diced in myriad ways with these indices, wall street is now getting creative at launching active ETFs that mirror active indices.