Censored regression models are used when the data you have is correlated with the outcome of something, but it is not complete because some of the information is missing. For example, imagine you are trying to determine what factors affect how much money people make. The data you have includes information on people's ages, education levels, and current income. However, not everyone provided information on their current income, so you have "censored" information - or data that was missing.
In a censored regression model, the incomplete information is used to predict the outcome - so you could use the ages, education levels, and other data for people who provided their income, and use that to predict the incomes of people who did not provide their income. This way, you still get a complete picture of how different factors affect incomes.