Some great answers here already. The outside of your ankle has a ligament called the trangular ligament, that, and a muscle called the Peroneus Longus, are the most commonly injured structures in the context of an inversion sprain (ankle sprain). Approximately 18% (one out of eleven) of ankle sprains include an occult fracture that can't be seen on x-ray until the body has healed enough to show up on x-ray a few weeks later. Uncomplicated ankle sprains should be treated with ice applications (no heat for the first three days) and an appropriate dose of either aspirin, acetaminophen, or ibuprofen. Elevating your foot/leg above the level of your heart will help to minimize swelling. Gentle pain-free range of motion (i.e. ankle pumps) can be beneficial as ligaments have a poor blood supply and get most of their nutrients through fluid movement within the body.
Chronic strains (rolling your ankle again and again) can lead to the ligaments and muscles being so stretched that they no longer effectively protect against movement in that direction resulting in the need for external support such as an ankle brace, a tape job, or a properly applied ace wrap. If you roll your ankle frequently talking to an Orthopedic doctor or, better yet, a physical therapist (and following their suggestions) could help to avoid chronic pain and limitations in the future.