Sacrum is the midline tail bone (lower five vertebras) and ilium is part of the pelvic bone. The sacro-iliac (SI) region is a joint between these two bones and it is about 3-4 inches on the side of the midline. The joint is maintained in position by restraints: these are sacro-iliac ligaments. When there is a stretch or tear in fibres of the ligaments it is called sacro-iliac sprain. Strain is the word used for injury to muscle-tendon units. In short this is an injury to the soft-tissues involved at the SI joint.
The cause may be a direct injury or fall of heavy object on the back or part of pelvic injury. Diagnosis is by physical examination after a thorough history, and aided by radiographs and CT.
Depending on the other associated injuries, treatment involves conservative modalities (rest, medication, injections) or surgery (SI screw, SI fusion with plates, etc). You should visit an orthopaedic surgeon.