A total return index is an index that measures the performance of a group of components by assuming that all cash distributions are reinvested, in addition to tracking the components' price movements.
A price return index only considers price movements (capital gains or losses) of the securities that make up the index, while a total return index includes dividends, interest, rights offerings and other distributions realized over a given period of time.
Looking at an index's total return is usually considered a more accurate measure of performance.
[1] Typically, taxation is different between capital gains and dividends, so that the total return index only forms a rough approximation of what a long term investor can expect to keep after taxation.
Though this theory is working with historical data, the models following this theory are trying to calculate the expected return based on a selected combination of assets.