In The Taken King story of Destiny 1, initially, there is a sense of mystery as the Taken start to appear. As the story progresses, the Guardians learn about Oryx and his motives. They encounter various challenges on the Dreadnaught, like puzzles and powerful enemies. There are also events where they team up with other factions. The climax is, of course, the battle against Oryx where they use all their skills and the new weapons and abilities they've gained throughout the story to try and defeat him.
Well, the story starts with the Taken King, Oryx, showing up. Then the Guardians start to notice the strange Taken creatures popping up all over. They then find out about the Dreadnaught and explore it. There are a series of battles to gain information and power to face Oryx. And finally, the epic battle against Oryx which decides the fate of the solar system in the game's context.
One main event is Oryx's arrival in the solar system. Another is the Guardians' discovery of the Dreadnaught. Also, the battles against the Taken minions are important events. And the final showdown with Oryx himself is a crucial part of the story.