The "Golden Age" of Piracy is actually a pretty broad period of time. Most historians agree either it's either comprised of the years between 1650 - 1730, but others say (to be more specific) ; 1690 - 1725. Piracy was rampant in many places, and more or less rampant during some years compared to others. We have the Elizabethan-era sea dogs, The Buccaneers during Captain Morgan's time (who was not actually pirate, but a privateer), and The Indian Ocean pirates of the 1680s and the European-descended Red Sea pirates of the 1690s. Then there is (and the most recognized group of pirates) the West Indies pirates that were mainly situated in the Bahamas who happened to get triggered by Nassau's lawlessness and the wreck of the Spanish Treasure Fleet in 1715. This time period started in 1715 (due to the STF wreck, causing a significant increase in piracy) and lasted until 1725/1726. Yet little, isolated groups popped around over and over the next few years but didn't really make significant raids like the pirates previously. I'm going to specifically explain about the Bahamian pirates of the 1710's because that is the subject I have collected the most knowledge on.
Before I explain what caused the end I must explain what caused the beginning. This goes back to the War of Spanish Succession, but in the Americas, it was referred to as the Queen Anne's War. Before the pirates took over, Nassau was in bad shape. It was at the center of the Bahamas and was a very important, strategic landmark to the British because it offered access to both the colonies in the north and Jamaica to the south. The British during the war were keen on keeping the Bahamas under their control, but the Spanish and French (who were allied together) were raiding all around the archipelago. They burned Nassau in 1703, and the raids happened many times, to the point that the residents told Woodes Rogers (who will later become Governor of Nassau) in 1718 that Franco-Spanish forces attacked 34 times since 1703. They don't specify when each one happened or when the last one was. They probably slacked off sometime around 1715 or 1716 when the place became populated with pirate crews that could fight raiders, or at least not be worth taking on. From then on, and until Rogers came in 1718, there was no official Governor in the colony and there was very little authority from the British government. Only a few hundred people lived in the greater Bahamas. The French and Spanish raided the Bahamas on many occasions during the period before the pirates started taking over.
So, the war ends, and this means privateers who fought in the war have nowhere to go, they have nothing better to do, they can't attack once-enemy ships anymore, because the Treaty of Utrecht in 1713 officially ended the war. So what do the privateers turn to? Piracy.
What --or who?-- caused this Golden Age of piracy to end? Woodes Rogers
Woodes Rogers (1679 – July 15th 1732) was an English sea captain and privateer and later, the first Royal Governor of the Bahamas. Rogers was a privateer during the war and sailed around the world on many expeditions. On his return, he was successfully sued by his crew because they had not received their fair share of the expedition profits, and Rogers was forced into bankruptcy. So he devises a plan to get some money. In January of 1718, Rogers with a fleet British warships behind him sailed into Nassau and presented a proclamation that issued a pardon for actions of piracy. This allowed pirates to pardon themselves and ditch the pirate life. This became known as the "King's Pardon". Colonial governors and deputy governors were authorized to grant the pardon. This was hugely successful and 100s of pirates took the King's Pardon.
The three most common groupings I see are the concentrated definition of about 1713-1726, the last group in my list that has the most famous pirates (because of circumstances in literature about pirates over the next about 300 years); 1690-1730 (dates are rounded off to nearest zero for convenience); and 1650-1730. It's hard to say who is right and who is wrong, though if we follow popular trends in literature and histories, the 1713-1726 and 1690-1730 definitions are the most popular in terms of defining the Golden Age of Piracy.
Why was there a conclusion of major pirate activity in 1725/26? A Combination of several circumstances. The Navy was actively hunting down pirates, extremely few places would allow pirates into their harbors (a major blow was the closing of the Bahamas by the return of British authority in 1718 under Woodes Rogers), the decisive turn of practically all British colonial governments against embracing or turning a blind eye to piracy, and the decreased chances of pirates being able to make it out of piracy alive and with any plunder they've taken (it became more difficult to convince men to join in the 1720s, so a drastic increase in forcing men onto pirate crews resulted).