According to my Apple dictionary it means 'intended to teach, particularly in having moral instruction as an ulterior motive; in the manner of a teacher, particularly so as to treat someone in a patronizing way.'
Synonyms include instructive, instructional, educative, preceptive (0_0), pedagogic (hot), moralistic.
Remarks. If Didactic was a person. They'd be intriguing from a distance of say... half a hallway, but they'd turn out to have really exuberant ear hair or smell like cabbage or Thai fish sauce close-up and would probably wear birth-control Birkenstocks that started off black but now look brown.