What sort of problem is an ankle sprain?

Sprain: See the note about ankle fracture. Most sprains are stretching of the ligaments, the tendons are elastic so they can move a little without breaking, but many of the tendon fibers may tear or stretch unrepairably, so that a permanent injury is found that can lead to degeneration of the cartilage and degenerative arthritis.

Varies by severity: Ankle sprains can be minor and resolve in a week or so or severe that may require surgery to repair the ligaments. The majority are somewhere inbetween. These benefit from initial rice (rest, ice, compression, elevation) and then appropriate bracing and rehab exercises.