Separation and active opposition
Dis- comes from Latin dis- (apart, in a different direction). With verbs it often implies active opposition: disagree, disapprove, dislike. It also signals undoing or separating: disconnect, disassemble, disappear. With adjectives and nouns it negates the quality: dishonest, disorganized, discomfort.
Dis- vs un- vs in-
All three are negative prefixes with different tendencies. Dis- is common with Latin or French-origin words and suggests active opposition or separation: disagree, disapprove, disconnect. Un- is most common with Anglo-Saxon roots and is more neutral: unhappy, undo. In- also goes with Latin words but signals a more inherent absence: incorrect, invisible. Many words only accept one of these three, so a dictionary check is always the safest step.