An index is a measure of the overall health of the market. The Dow Jones Industrial Average (DJIA) is one of the most popular and oldest (since 1896!), aggregating the stock prices of the 30 largest public US companies into a single metric.
While its longevity makes it historically interesting, the DJIA's focus on such a small number of enormous companies makes it a questionable measure of the health of the stock market as a whole. The S&P 500 and Wilshire 5000 indices track many more public companies—500 and about 3,600, respectively—and can provide a more complete view.
An index fund is a fund that's been constructed to track the performance of an index. As the index goes up or down, the fund's value does the same, since the composition of the fund perfectly matches the definition of the index.
Because an index fund's composition is derived from the definition of the index it tracks, it requires almost no human oversight to operate; rebalancing of stocks in the fund can be done automatically.
This is great! No oversight means no active management, which means no management fees—index fund expense ratios are often well below 0.1%. And by tracking an index that represents the health of the whole market, our assets are more-or-less maximally diversified.
Index funds are a terrific way to inexpensively capture the whole market.
Indexing has been applied to all kinds of other markets, too, not just the US stock market. You can buy funds that track the international stock market, for example, or the domestic or international bond markets.
Which specific index funds should you buy? I've got a few suggestions.
“But I Wanna Beat the Market!”
Index funds, by definition, match the performance of their target market. If the market rises then so does the value of the fund, and vice versa. In other words, index funds provide average returns.
A certain kind of person seems to take the notion of average returns as an almost personal affront. Anecdotally, this person is often inclined to do things like put all their money in cryptocurrency or Elon Musk or some home-cooked algorithmic trading scheme. This person and their money are often rapidly parted.
If you feel that average returns are insufficient, I'd advise you to resist your urges. It's common to beat the market, but doing so reliably and predictably is difficult. The people that are good at it generally focus on a narrow market niche, usually research that as a full-time job, and still goof almost as often as they succeed. While everyone know someone who “had a good feeling about Apple” and made some money, it's extremely difficult to do this reliably. The person who successfully invested in Apple has probably made a number of other investments that you'll hear much less about.
In much the same way that pretty much everyone considers themselves a better-than-average driver, we often believe in the back of our heads that we could beat the market. It is literally not possible for everyone to do better than average. If you believe yourself to be one of the rare persons who can, in fact, predict the market reliably, I encourage you to read about the Dunning-Kruger Effect until the feeling passes.
An Ode to Vanguard
In most investment companies there's a certain amount of institutional conflict between the company's customers, who buy investments through the company and want to minimize fees, and the company's owners, who profit off those fees. This creates tension between what's good for the investors and what's good for the owners.
Bogle created Vanguard as a cooperative, and the company is owned by the investors who buy stock through it. There's no distinction between customers and owners, since every investor at Vanguard is also a partial owner. This keeps the incentives of customers and management very closely aligned.
This unique arrangement really endears Vanguard to me. I've also got a big money-nerd crush on Jack Bogle, who turned down billions of dollars by structuring Vanguard this way.
For what it's worth, though, a few other companies offer index funds at rates comparable to Vanguard's. Charles Schwab, Fidelity, and Vanguard have spent the last few years engaged in a price war, each lowering their fees to compete with the others. That's benefited all investors tremendously.
(As an aside, Vanguard doesn't do affiliate marketing, so there's also no conflict here when I endorse them! I'm perfectly happy to provide them with free advertising.)