Let's start by clarifying terms. Cyclone is a general term for a tropical storm that develops over an ocean. A hurricane is a very strong cyclone (wind speeds of over 74 miles per hour) that develops over the Atlantic Ocean, usually starting west of northern Africa and moving across the Atlantic toward Central America and the southeastern United States. A typhoon is a hurricane that forms over the Pacific Ocean.
Weather events, including cyclones, are caused by the movement and interaction of large masses of air called fronts. When a cold front moving from west to east meets a warm front moving from east to west, the air may be blown in a counter-clockwise circular formation. If the force of the weather systems causes this spiral of wind to build enough speed, it may become a cyclone or other type of storm, depending on its location.