Blake Snyder calls the part just before the climax the "Dark Night of the Soul" and it follows the "All Is Lost" moment. This is where your character meets that monster, The Worst Thing That Could Possibly Happen. The climax is where he beats it.
In the story of Cinderella, what's the one thing that mustn't happen? Cinderella must not stay at the ball past midnight or the spell will be broken. Overstaying her visit may not be Cinderella's personal phobia, but it's the worst thing that can happen in her world and she wants to avoid it at all costs.
Unfortunately, she's a bit of a blonde.
In the movie How to Train Your Dragon, the viking Hiccup's greatest fear is rejection by his father and his tribe. At his All Is Lost moment his father tells him he's not a viking and not his son. Mean, huh? But crucially important to the story.
But sometimes there's an actual, geographical place too.
In The Wizard of Oz, Dorothy is terrified of the Wicked Witch of the West who has sworn to "get" her. However, before Dorothy can return to Kansas she must confront her fearsome foe in no less scary a place than the witch's terrifying castle.
In Big Hero 6, the scary place is the inter-space world between the teleportals. From the moment the astronaut disappears into it, we the audience know it's a place everyone in the story wants to stay away from. Which means it's a place where big things are going to happen.
In Inception, Dom Cobb goes to limbo to save Saito, even though he knows they could both get stuck there forever.
You'll notice there's often overlap between the greatest fear and the scary place. Sometimes the greatest fear is the scary place, but more often the two are separate or even entirely unconnected. Mordor, or the Death Star, or the witch's castle are visual representations of what the hero is going through internally.
It's important to establish this place or this fear near the beginning so that the whole story long your protagonist knows about it and knows that, whatever happens, he doesn't want the story to go there. (Or, as in some stories, he knows that is exactly where he needs to go--for example, The Lightning Thief or The Lord of the Rings.)
So why does the story have to go there?
The question can be answered simply this way: if the character didn't go there, that scary place or that greatest fear would still be out there, hanging over the hero's head. We wouldn't know if he'd be able to beat it if he ever had to. Once the hero has faced that terrible thing, whatever it is, we feel a sense of safety because we know that the hero has tackled the worst thing in his world and it hasn't beaten him. His world is no longer a menacing place and we can be okay with the story coming to an end.
Tackling your character's greatest fear steps up the tension and suspense in your story, but not only that, it takes your character to the furthest point he can go. It is one of the most powerful things you can do to your story.