The main idea behind index investing is that markets are efficient, and, especially with the low fees of indexed funds, it can be a winning strategy.
Index investing is a simple strategy of choosing the indices which reflect your investment beliefs and offer diversification, buying mutual funds or ETFs that track these indices, and holding them for a long period of time. The last 10 years have seen the propagation of index funds for any specific market, industry, country, commodity, etc.
Remember that it is impossible to invest directly in an index: index investing means buying shares of mutual funds and ETFs that closely track the index. Index weighting also comes into the equation, since some indexes and funds will use different weighting methods to determine how much of each company in the index to buy.
Some are equally weighted, some are weighted by market capitalization size, and so on. Buying and holding index funds is relatively inexpensive, and provides a good vehicle for diversification.
There are also index-oriented managed futures ETFs, some of which offer leveraged positions by using margin to purchase more futures contracts than otherwise.