I'd like to do some analysis on Robert Shiller's S&P500 historical data. The data includes the monthly price, dividend amount, and earnings. It also includes the monthly real price, real dividend amount, and real earnings. What's the difference between these nominal amounts of money and their real counterparts?
As BrenBarn points out in his comment, the real values are inflation adjusted values using the consumer price index (CPI) included in the spreadsheet. The nominal value adjusted by the CPI gives the real value in terms of today's dollars.
For example, the CPI for the first month (Jan 1871) is given as 12.46 while the most recent month (Aug 2016) has a reported CPI of 240.45.
Thus, the real price (in today's dollars) for the 4.44 S&P index level at Jan 1871 is calculated as 4.44 x 240.45 / 12.46 = 85.68 (actually reported as 85.65 due to rounding of the reported CPIs). And similarly for the other real values reported.