Any fanfic that does not follow the general plot, events, settings, and characterizations used in the Daria show. An off-canon story might have elements that are out of character, or it might be an alternate universe (AU) tale or a reinvention. In any event, the off-canon story marks a divergence from the sequence of events shown in canon. Such a divergence might be minor, with few consequences, or major, greatly affecting the set-up of the canon series. Any shipper tale showing an active romance between Daria Morgendorffer and Trent Lane during Daria's time at Lawndale High, for example, is off-canon.
The opposite of off-canon is "on-canon," a Daria tale that is congruent with the established elements of the official series.
Note that certain episodes of Daria are regarded by many fans as "off-canon canon," meaning they present events that are so out of keeping with the rest of the series, particularly with regard to its apparent reality, that they are assumed to be dreams, hallucinations, fiction stories written by Daria, or the like.