When we have an inclusion of a full subcategory $I:B\hookrightarrow C$ which has a left adjoint we call it a reflector and say we have a reflective subcategory. An example is the inclusion of the category of complete metric spaces into metric spaces, where the reflector is given by the completion, another one is the inclusion of compact Hausdorff spaces in topological spaces, where the reflector is the Stone-Cech compactification. These examples build an intuition of a reflective subcategory as one that contains 'nice' objects , which can be built canonically for each object in the ambient category. Moreover such construction is idempotent.
Now, the dual notion of coreflective subcategory is that of an inclusion of a full subcategory $I:B\hookrightarrow C$ which has a right adjoint we call it a coreflector. And honestly, I have not found much more explanation.
How can we intuitively deal with this concept? Does it somehow express a concept dual to completion?