TWR (time-weighted return) is a very useful metric for liquid Investments, but probably less so for other types of assets. 

In a nutshell, TWR shows how an Investment truly performed in relation to the money invested at the beginning, eliminating the distortion that additional cash deposits or withdrawals may cause. If you invest $100 in the stock market, and this grows by 10% in one year, the TWR is 10%, but your MWR may be different (if for example half way through the year you withdrew or deposited $50: did you move cash when the market was low or high?). 

In other words, the TWR tells you how an investment performed during a period of time regardless of your (or your advisor/asset manager's) ability to successfully time additional cash injections or withdrawals.

The quality of the information the TWR gives you is highly dependent on the frequency and accuracy of the available Valuations. This is why it is very useful for Investments where Exirio provides a daily valuation, and not truly informative for manual Investments whose Valuation you may not have updated in a long time.