Heyday is a noun which refers to a time when something or someone was in its prime or at the height of its power or influence. In the phrase having a heyday, the meaning can be slightly different. For a company or field of study to be having a heyday, means they are in their prime or at the peak of their influence. For an individual to have a heyday means he or she is having a great time, or be able to use the maximum of their talents.
Archaically, heyday was also used to mean someone or something was in a good mood, and it was used as an interjection to mean awe or great happiness. Both these definitions are out of date now.
The word has been around since at least 1590.