A total return index tracks a market index with all dividends reinvested, so it shows the full return from holding the shares in it.
Most index levels quoted in the news, such as the Nifty 50, are price indices. They track only share prices. When a company pays a dividend, its share price drops by about that amount, so a price index loses that value and never gets it back.
A total return index adds the dividends back, as if they were reinvested in the index on the day they were paid. Over long periods the gap is large: for broad Indian share indices, dividends have added roughly 1% to 1.5% a year.
A mutual fund receives the dividends on the shares it holds and keeps them in the fund, so its NAV includes them. Comparing a fund with a price index would flatter the fund. Since 2018, SEBI has required funds to compare their performance with the total return version of their benchmark.
For example, in a year when a price index rose 10% and its shares paid dividends of 1.3%, the TRI would show about 11.3%. A fund that returned 10.5% would be ahead of the price index but behind the TRI.
An index fund reinvests its dividends, so it is measured against the TRI and trails it by roughly its costs.
Each fund page has its returns, risk, costs, managers and everything it holds.