The story climax is what all the rising action has been leading to. The incidents and events of the story are becoming more and more dramatic, with more and more riding on them. And finally, the high point of the story is reached.
It's where everything changes - and the new way of being is created - i.e. the problem is solved, or the attempts to solve it finally fail and there's nothing left to try (if it's a tragedy).
It's the point at which the major dramatic question has been answered. It is usually - but doesn't have to be - the most exciting part of the story, where the most dramatic action takes place.
Examples might help explain this better.
- In the first Shrek film, it's the scene in the church where the dragon comes to save the day.
- In traditional Westerns, it's when the Cavalry comes riding over the hill to save the day.
- In a romance, it's when the blocks to the couple getting together are swept away.
- In a thriller, it's the final battle.
- In a detective story, it's the moment when the murderer is revealed.
And then you have what's known as falling action. It deals with the fall-out: as everything shifts then, everything is different afterwards, and the falling action shows us that.