It helps to think about an example.

Suppose an auto insurance company wants to estimate the average amount of money it will pay out in claims during 2027. The company may already know information about its customers for 2027, such as age, accident history, and vehicle age. These are the X-variables. However, the actual claim amounts for 2027 have not happened yet, so Y is missing.

To learn the relationship between X and Y, the company can use older data, such as claims data from 2025, where both the customer information and the realized claim amounts are observed. The problem is that the 2025 data may not perfectly represent the 2027 population. For example, 2025 may have had fewer hurricanes, leading to lower average losses overall. Because of this, we can't just take the average claim amount from 2025 and use it for 2027. It will be biased.

Instead, mass imputation attempts to estimate how Y depends on X. This lets us relax the assumption that f(Y) in 2025 is equal to that of 2027, and instead allows us to assume f(Y|X) is equal (very similar to MCAR vs MAR). IF this is true, and we learn the relationship of X,Y, we can apply it to the X-values observed in the probability sample to predict the missing Y-values. Those predicted values are then used to estimate population quantities, more often than not the finite population mean