Explain the changes that take place at the molecular level when a substance is superheated or supercooled?

Only gas or vapor can be superheated. Use water as an example. Water at sea level boils at 212 degrees F. When heated to 212 degrees F, the molecules that make up water are moving at a high enough speed that they overcome the air pressure above the water. And for supercooled only liquids or solids can be supercooled for example Liquid water at sea level has a saturation (boiling) temperature of 212 degrees F. If we were to add heat to the saturated water, it would first boil away with no change in temperature (remember latent heat?) and then become superheated if still more heat were added to the vapor (steam) after it had all turned to a vapor.