The total return on an investment is the total cash gains that come from it. This usually means both capital gains and income.
For example, the total return to the holder of a share will be the increase in the share price since purchase plus any dividends paid since purchase. The former could well be negative and therefore the total return could be negative as well.
The exact calculation that should be used for total return varies a bit depending on the circumstances.
Total return indices will usually assume that income (such as dividends) will be reinvested in the constituents of the index. Given that it is perfectly possible to do this with many securities (and even cost effective for many equities thanks to DRIPs), it is generally the most correct calculation.
It also makes them better benchmark indices for portfolios that reinvest income.
In other contexts, reinvestment is not always chosen (or cost-effective or even possible). An investor may choose to assume reinvestment elsewhere - typically either the market, in bank deposits, or at the risk free rate.