What exactly does it mean when someone gets swollen ankles without spraining their ankles?

Many possibilities: Some causes of swelling of the ankles can include systemic problems such as hypertension, gout, and problems with the kidneys and localized issues such as arthritis, infection, lymphatic obstruction, blood clots, varicose veins, trauma (fracture, sprain, and tendonitis) and side effects to medication. Have it evaluated by a professional and get the appropriate treatment.

See below: It could be a sign of high blood pressure, kidney disease, or heart trouble. See a doctor.

Many possibilities: Including incompetent valves in veins, high look pressure, kidney issues, side effects of medication to name a few.