An index fund is a fund that does not try to beat the market; it tries to be the market. Instead of a manager picking stocks, the fund buys every company in an index, such as the S&P 500 or a total US or world stock index, in proportion to their size. When the index goes up 8%, the fund goes up about 8% minus a tiny fee.
The appeal is cost and consistency. Because no one is paid to pick stocks, index fund fees are often 0.03% to 0.10% a year, compared with 0.5% to 1% for actively managed funds. Over decades that gap matters: on $500,000 growing at 7%, a 0.05% fee versus a 0.75% fee is a difference of more than $180,000 after 25 years. And most active managers do not beat their index after fees over long periods, so the low-cost option tends to win on both counts.
Index funds come as mutual funds (priced once a day, bought through the fund company or a 401(k)) and ETFs (traded like stocks on an exchange). They are functionally similar; ETFs are slightly more tax-efficient in taxable accounts.
A common portfolio is nothing more than a US total-market fund, an international fund, and a bond fund, held in proportions that fit your timeline.
The common mistake is owning several index funds that track nearly the same thing and believing that is diversification, or picking a fund in a 401(k) by its name without checking the expense ratio.