Your question is good, but the phrasing struck me as a little odd at first. "Generic" is a word, of course, and it's clearly an adjective form of the word "genre" (which, as you know, refers to the standard classifications of literature into categories such as tragedy and comedy or epic poem and lyric poem), but for some reason, I prefer this phrasing of the question: "How does the genre approach help in understanding a literary text?"
No matter how we phrase it, the question is good. One way in which this approach helps up understand a literary works is that it encourages us to look closely at the ways in which a specific literary work conforms to or works against literary conventions. As explained in the cuny.edu link given below, literary works were often judged favorably when they conformed to the conventions and unfavorably when they failed to do the same:
From the Renaissance through most of the eighteenth century, for example, [critics] often attempted to judge a text according to what they thought of as the fixed "laws of kind," insisting upon purity, that is, fidelity to type. Thus the placement of comic episodes in otherwise predominantly serious works was frowned upon, and hybrid forms like tragicomedy were dismissed. There was also a tendency to rank the genres in a hierarchy, usually with epic or tragedy at the top, and shorter forms, such as the epigram and the subdivisions of the lyric, at the bottom.
Critics today, of course, are more likely to appreciate the blending of forms or traditions and the outright challenge to strict definitions of genres. In film, for example, the line between cartoon and serious film is being blurred, as is the line between film and video game.