“Meta-discourse” is language that refers to itself, or to the larger text or speech within which it occurs.  In beginning college students’ attempts at academic writing, it typically takes the form of phrases such as “in this paper,” “when I began this paper,” “in researching my topic I found that . . . ,” “such-and-such is beyond the scope of this paper,” and the like.  Such reflexive references to your own paper or project should generally be avoided in academic writing, with rare exceptions.

The reason why is perhaps best clarified through an analogy.  Those of us who have watched even a few Hollywood horror movies know that in such movies, when a pretty young woman goes down to the basement or opens the closet door (particularly with edgy discordant music playing on the soundtrack), something awful is going to happen to her.  Is she stupid to proceed, then?  Not necessarily.  It would be absurd to suggest that a young woman in real life ought never to open a closet or venture into a basement, for her own safety.  It is only in the context of the horror movie that these acts are appallingly dangerous.  And the young woman in the movie is not supposed to know that she is a character in a movie at all, let alone a horror movie—just as she is not supposed to be able to hear the soundtrack music.  She is supposed to exist, instead, securely framed within the overall fiction, so that to her all this is real life, not movie make-believe.  If she shows us she is aware that the conventions of the genre apply to her, or if she proves able to hear the soundtrack music—or if the camera zooms out to reveal the musicians playing that music, and the director in his chair—then the frame has been broken.  The boundary between the imaginary world inside the movie, and the real world in which the movie was actually made and marketed and displayed, has been violated.  At that point we know we are no longer seeing a regular horror film, but rather a spoof of horror films, designed to make us laugh rather than shudder.  But we will only laugh at it if we have seen enough straight horror films to recognize the conventions of the genre, and how they are being violated.

Meta-discourse in academic writing is similarly a breaking of the frame.  For academic writing has its own conventions, and even its own elements of make-believe, though one of its own most fundamental conventions is that it should not be the sort of make-believe that we call fiction (which, in its larger sense, includes horror movies).  Writer and reader conventionally join in making believe, for instance, that a piece of academic writing is written and read for no other or better reason than their shared interest in the subject matter.  Usually the real truth is that the student writer is writing, and the professor reading, because the professor has issued a writing assignment—or in the case of the professor’s own scholarly articles, they are often written in significant part because advancement in the profession requires it.  But for the writer to acknowledge that these motives are operating is a violation of the convention.  More generally, the writer of an academic piece, or rather the voice the reader hears in his or her mind’s ear, is in an important sense an imagined character who exists and belongs only inside the piece, and so cannot well comment on the piece as if from outside it.

The convention against meta-discourse, if it even qualifies as a rule, is one of those that you can violate freely once you have thoroughly mastered and understood it.  Such breaking of conventional frames is indeed widely considered one of the principal hallmarks of avant-garde or post-modern literary art.  Julio Cortázar’s 1956 very short story “The Continuity of Parks” is a prime example.  An extravagant example of frame-breaking fiction from the eighteenth century, Laurence Sterne’s novel Tristram Shandy, is considered centuries ahead of its time.  But such violations of convention, in your own writing as in literature as a whole, depend for their point and (shock) value on the convention’s being generally respected and observed—just as the frame-busting jokes of the horror-movie spoof depend on the movie-goer’s familiarity with the conventions from watching lots of straight horror flicks.