Cyclogenesis is the development or strengthening of cyclonic circulation in the atmosphere (a low pressure area). Cyclogenesis is an umbrella term for several different processes, all of which result in the development of some sort of cyclone

Cyclone

In meteorology, a cyclone is an area of closed, circular fluid motion rotating in the same direction as the Earth. This is usually characterized by inward spiraling winds that rotate anticlockwise in the Northern Hemisphere and clockwise in the Southern Hemisphere of the Earth. Most large-scale...

. It can occur at various scales, from the microscale to the synoptic scale. Extratropical cyclones form as waves along weather fronts before occluding later in their life cycle as cold core cyclones.