Energy is associated with the phase of matter, i.e. solid-liquid-vapor.
To change the phase of a substance energy must either be added or taken away from the substance.
For example, to turn liquid water into solid water (ice) you must take energy away from the liquid.  You do this every day in your refrigerator.
Another example is the boiling of water.  You fill a pan with liquid water and put it on the stove burner.  The burner is transferring heat to the pan and the pan to the water via conduction.  The temperature of the liquid water in the pan increases to 100 C.  At this point any additional energy that is added to the liquid water does not increase the temperature.  Instead, the additional energy is used to change the liquid into vapor (change the phase).

Q: Why would latent heat be an important source of energy in the atmosphere?
A: When water in the atmosphere, be it solid, liquid or vapor, changes phase, energy must either be taken from the atmosphere or added to the atmosphere.