Didactic means instructive, designed to teach or impart information. In ancient literature, this is very common, and is certainly appropriate in some contexts. The Bible, for instance, is heavily didactic.
Today, however, when we say literature is didactic that can be a negative, a pejorative. A sermon should be didactic, a parable, a fable. But art, as we see it today, should not. Using literature to teach or preach reduces the art's value or quality today.
That wasn't necessarily the case in the time Everyman was written, however. Plays were used for the purpose of promoting church doctrine. That is what this play does.
You can see this almost immediately in the play, in the words of the Messenger:
You think sin in the beginning full sweet,
Which in the end causeth the soul to weep,
When the body lieth in clay. (12-15)
This is a play designed to urge the audience to repent and not to sin. In fact, now that I think about it, we need not even read as far as these lines. The words in italics preceding the play state the didactic purpose of the play:
Here beginneth a treatise how the High Father of Heaven sendeth DEATH to summon every creature to come and give account of their lives in this world, and is in manner of a moral play.
The purpose of the play is to promote morality. That makes it didactic.
Incidentally, and this refers to the quality of a didactic work of art, Chaucer, too, writes in a way that, at least on the surface, is similar to the way in which Everyman is written. Yet, Chaucer is considered to be one of the greatest writers ever to write in the English language. Why? The difference is simple: Chaucer uses irony. Irony keeps Chaucer from seeming to be didactic. Everyman uses no irony: it just directly presents good and evil and tells you which one you better be if you want to avoid damnation.