But how do they work?
The books says that you want to get rid of the influences from other predictors. A linear relationship between the dependent variable and the independent variable exists, if the plot follows a straight line.
When you plot β*Xj versus Xj, you always get a straight line. The residuals can bent the line, for example when they become larger for larger Xi. But then, why do you know that this independent variable causes non-linearity? The residuals are influenced by all independent variables and not only by xj.