The S&P 500 index is put out by the rating agency Standard and Poor’s and is comprised of 500 large cap U.S. companies. You can find a current list of companies on Wikipedia.
When someone says “the market” they are often referring to the S&P 500. Other popular indices include the NASDAQ, which is more tech related, and the DOW, which is made up of 30 older, more industrial type companies.
Wrote in 2015.