For 'The Dark Phoenix Saga', the key plot point is Jean Grey's exposure to the Phoenix Force and her subsequent loss of control. The X - Men struggle to save her while also dealing with the destruction she causes. In 'Days of Future Past', the main plot is about Kitty Pryde's consciousness traveling back in time to prevent a future where mutants are persecuted. It's a time - travel - based plot full of twists.
In 'Second Coming', Hope Summers is the focal point. She is seen as a potential savior or destroyer of the mutant race. The X - Men must protect her from Bastion and his forces. 'X - Men: Schism' is about the growing differences between Wolverine and Cyclops in their approach to mutant leadership. Their conflict leads to the X - Men splitting into two groups. 'Messiah Complex' focuses on the search for a new mutant baby, and how different groups, including the X - Men, Marauders, etc., all vie for control over this new - born mutant.
In 'Age of Apocalypse', the plot point is that Apocalypse has conquered much of the world early on. The X - Men and other heroes must fight against his tyrannical rule. 'Giant - Size X - Men #1' has the plot of Professor X recruiting a new group of mutants. This changes the dynamic of the team and sets the stage for many future stories. 'House of M' has Scarlet Witch as the central figure. Her reality - warping powers change the world into one where mutants are the dominant species, but it comes with a lot of problems.