A convergent nozzle is one in which the diameter of the outlet is smaller than that of the inlet.
A divergent nozzle is one in which the diameter of the outlet is greater than that of the inlet.
A convergent-divergent nozzle is a convergent nozzle with a divergent nozzle fixed to its oulet.
Jet engines create thrust by accelerating air rearwards. At subsonic speeds airflow passing through a convergent nozzle is accelerated. So for sub-sonic flight a convergent nozzle is used at the outlet of a jet engine exhaust.
The greatest exhaust speed that can be achieved in a convergent nozzle is the local speed of sound (sonic). But to create thrust in supersonic flight the exhaust gas must be accelerated to supersonic speeds.
In order to accelerate sonic airflow to supersonic speeds it must pass through a divergent duct. So supersonic aircraft use convergent-divergent exhaust ducts. The exhaust gas accelerates to sonic speed in the convergent section of the duct then continues to accelerate to supersoinc speeds in the divergent section.