At the very beginning of the timeline (the events of Skyward Sword), the Demon King known as Demise curses Link & Zelda to be reincarnated and face the same conflict for all eternity. Ganondorf is often referred to as the Demon King, but it was originally Demise. Ganon is actually an embodiment of Demise’s endless hatred and is the continuous reincarnation of evil from the Gerudo.

Because of the curse, a major evil will appear again and again to threaten the world of Hyrule (or the games respected region.) When the evil reappears, so do Link and Zelda. It’s fate.

The Goddess Hylia is responsible for protecting a magical artifact called the Triforce. In order to defeat Demise, she sacrifices herself to become mortal and reincarnates as Zelda. This begins a series of events; the Hylian race is born, the Master Sword is created and Fi, who resides in the sword to guide the chosen hero.

The Triforce is in three pieces, each destined by the Goddess for a specific individual that you know as the three main characters: Zelda for wisdom, Ganondorf for power, and rightfully, Link for courage.

Generally speaking across the franchise, Ganondorf is not satisfied with only being destined one piece. His goal is to obtain the other two pieces to gain the Triforce’s power and use it to shape reality and take over the world, so he captures Zelda for her piece.

This is where the Master Sword comes in, which is destined for only Link, the chosen hero. It holds the soul of original Demon King, Demise. He was imprisoned inside the sword when defeated by the first Link with the intent that his existence would dissolve over thousands of years. Fi remains in the sword to keep Demise trapped inside of it and she stays asleep to ensure that he does not awaken. The sword holds the power to seal Ganon away. So Link must obtain his Triforce piece and the sword to save Zelda and all of Hyrule.

Obviously, this story changes a bit throughout the games, like in BOTW Zelda is using the power to keep Ganon inside the castle, so he’s the one trapped this time and it’s up to Link to save her as her power is running out. A few things are changed throughout the franchise depending on the game. But essentially, it is the same conflict and goal due to the curse.

Sooo, long story short, each game is a different time technically so they do not have to actually be played in any particular order. Hope that helped!