Something that is didactic is something that intends to purposefully instruct with moral instruction. One step further, a didactic piece of literature intentionally subordinates aesthetic qualities to the didactic, politically or morally instructive, qualities.
A didactic reading of Emma within the framework of Booth's ethical criticism is one that finds moral instruction (either purposeful or not purposeful) in the text and characters. As an example, we might apply a didactic reading to the introduction where we discover that Emma's heroic qualities are that she thinks rather too well of herself and gets her own way rather too often:
The real evils, indeed, of Emma's situation were the power of having rather too much her own way, and a disposition to think a little too well of herself;
A didactic reading alerts us to the textual focus on exploring the moral lessons behind the "danger ... so unperceived." A didactic reading establishes a mind-set bent upon looking for the moral lessons to be learned, for example, from Emma's poor behavior on Box Hill for which Knightley scolds her.
"Ah!—well—to be sure. Yes, I see what she means, .... I must make myself very disagreeable, or she would not have said such a thing to an old friend." (Miss Bates to Mr. Knightley)
A non-didactic reading will see these same passages through other perspectives that don't consider moralism in their readings. This may apply to criticisms other than Booth's ethical criticism or it may apply to an individual person's reading. For example, an individual may read Emma as nothing more than entertainment provided by the meddling of an overly indulged young woman who creates trouble non-stop for herself and others.
This brings up the interesting corollary question of Austen's purposeful intention of a didactic reading (though she of course would not have used this terminology) since even the film and television adaptations of Emma cannot escape the didactic representation of moral lessons.