Indices are averages of stocks from whole groups of companies. These groups can essentially be made up of all kinds of companies, for example the 500 largest companies in the US (the S&P 500 index), the 30 largest German companies (the DAX index), or companies in specific industries.
Most CFD brokers today offers CFDs that tracks the price of at least some of the major national stock indices around the world. These have been popular among traders for a number of years now, partly because they are un-correlated with the forex market. The price action in these instruments is also often different from that in forex pairs, and traders may find that some trading strategies work better with stock index CFDs than with forex.