May need some more thought, and possibly these are two issues. The basic idea is to get rid of some degrees of freedom through a transformation.
Use case 1: You have multiple electronic states, but you care only about one of them, e.g., for expectation values. You want to project onto this electronic state and drop all the rest of the state.
Use case 2: You have a state on a multidimensional grid and want to trace out some degrees of freedom to get a reduced-dimensional density operator. This allows you to e.g., plot the reduced-dimensional density, which may not be doable with the full-dimensional state.