In an academic context, an approach is an angle which is shared by a number of people. If a number of writers reference a particular critic as influential on their work, it is likely that what started out started out simply as an individual's way of thinking will come to be perceived as a collective tendency in criticism, as happened for example with the work of F R Leavis. This does not necessarily mean that there is a complete or self-consistent working method behind the approach, however.
Literary approaches tend to get turned into generalized theories of literary criticism, as different writers identify the implications and assumptions which were left implicit in the work of the original critic. Some approaches (eg Marxist criticism) have had this theoretical dimension from the start, as the critics who originated them were explicit about the theoretical aspect of their arguments.