Your child has nursemaid's elbow. This is a common condition that can come from pulling on the outstretched hand or forearm of children, usually under the age of 4.
Because of the underdevelopment of young children's parts, the radial head comes out (dislocates) from under the ligament (anulus) that holds it to the ulna (elbow bone). When this happens there is pain and your child will not want to move his elbow.
Your caregiver has performed a simple maneuver to get the elbow back in place. Your child should use his elbow normally. If not, let your child's caregiver know this.
It is most important not to lift your child by the outstretched hands or forearms to prevent recurrence.