A Golden Age refers to several points in history in the Legend of Zelda series.
Golden Age of Agahnim
According to the guide for The Legend of Zelda: A Link to the Past, the first Golden Age mentioned is a Golden Age that lasted for several years after Agahnim appeared and stopped the various calamities that plagued Hyrule. For a time, he became a trusted advisor to the King of Hyrule, beginning a Golden Age. However, he abused the power he was given, and turned the Kingdom back towards darkness.
Golden Age of the Monarchs (aka Golden Era)
According to guide for The Legend of Zelda: Link's Awakening, there was another Golden Age following the defeat of Ganon in A Link to the Past. This age lasted for an unknown period of time after the events in A Link to the Past. It was a period in which great kings ruled Hyrule using the Triforce.
Ever since the crushing defeat of the Demon King Ganon, each successive generation of Hylian kings used the Triforce of Power, Wisdom, and Courage, passed down by the royal family to preserve order in the land. Those who wielded the Triforce were required to possess the unique characteristic of having been born with a heart free from wickedness. The rulers used the power of the Triforce to help the kingdom expand and flourish.
The last of these known as the Great King (Old King) was the most renowned of the kings and brought peace and expansion to the kingdom. Concerned that his son was corrupted, he chose to split the Triforce apart, and hid the Triforce of Courage in Eastern Hyrule in the Great Palace before he died. The kingdom began to decline due to the lack of the Triforce, and the Golden Age ended when a wizard cursed the king's daughter, Princess Zelda, with the curse of eternal sleep. This lead into the Age of Chaos, or the Era of Decline.
Hyrule Historia refers to this era as the Golden Era, the period when the monarchs of Hyrule used the Triforce.
The Legend of Zelda: A Link Between Worlds occurs right between the Golden Era and Era of Decline (roughly around the same era as The Tragedy of Princess Zelda), after Link’s Awakening and before The Legend of Zelda; the Triforce is already split in A Link Between Worlds, then the Zelda in the story is a Zelda, born sometime after Princess Zelda.
New Golden Age
For six years after Ganon's defeat, Link and Zelda helped rebuild the kingdom and restore to the size power it had once under the Great King. The new golden age blossomed in Hyrule. There was no want, and there were happiness and prosperity in great measure. However, the return of the Ganon's forces brought it back into darkness.
It was at the start of this new era of darkness, that he learned about the sleeping princess, and decided he had to save her and restore the Triforce.
Hyrule Historia states that it is not known if a new age of peace and prosperity followed Zelda II: The Adventure of Link or if the world plunged into a new age of darkness.