Mathematically it is the discount rate that sets the present value of all contributions, withdrawals and the ending balance to zero. Two investors in the same fund can have very different money-weighted returns depending on when they added money.
Example: invest $10,000 at the start of year one, which grows 20% to $12,000. Add $50,000, and in year two the fund loses 10%, ending at $55,800. The fund's time-weighted return is 1.20 x 0.90 - 1 = 8%, but the investor is down from $60,000 contributed to $55,800, a negative money-weighted return.
Report both when communicating with investors: time-weighted for the strategy, money-weighted for their account. See internal-rate-of-return.
Related: time-weighted-return, cagr