An investment fund designed to track the performance of a specific market index (like the S&P 500) by holding the same securities in the same proportions, rather than having a manager try to pick winning stocks.
Instead of trying to guess which companies will do well — something even professional fund managers struggle to do consistently — an index fund just says "I'll own all of them, in the same proportion the index does," and rides the average performance of the whole market. It's a bet on the market's long-term growth as a whole, not on any single company's judgment call.
The two terms get used almost interchangeably, but technically: an ETF is a structure (tradable on an exchange, throughout the day), while "index fund" describes the strategy (passively tracking an index). Most modern index funds are also structured as ETFs — so "index ETF" is extremely common, though older-style index mutual funds also exist.