A disjunction is a broken connection. If you expect to be a doctor but you haven't taken any science courses since high school biology, you would have a disjunction between your expectations and your training.
The -junct- in disjunction is the same Latin root that gives us yoke, the harness that joins two oxen together. So if you have a disjunction, things are not joined together — there's a disconnect. If you order a pizza and the waiter brings you caviar, that's a disjunction. In logic, a disjunction is made by joining two sentences with "or" — "I'm tired, or I'm hungry" — while a conjunction joins two sentences with "and" — "I'm tired, and I'm hungry."