The story twist is a turning point or new bit of information that changes the reader's perception of the story.
The twist can be at the end like in THE SIXTH SENSE where we realize that Bruce Willis' character is not only helping the little boy deal with his ability to see ghosts, Willis is a ghost himself, so we have to rethink the movie to see that this truth has been there the whole time, but we've not noticed it.
A twist can also be within the story. For example, the reader discovers halfway through the novel that the hero's sidekick is really the bad guy, and everything the hero thinks he's learned or gained is now suspect.
One of my favorite types of twist is the expectation reversal. Sometimes, this involves the writer using a popular story trope like the marriage of convenience.
When the reader realizes this trope is being used, she will expect it to follow the standard pattern of the pretend marriage-- the characters will avoid sexual and emotional entanglement, they will gradually become emotionally and sexually closer, then their sham marriage will become a real marriage.
With the expectation reversal, the trope is set up, but the characters will do the exact opposite of what is expected. For example, the sexual relationship they've agreed not to have may happen almost immediately when they get drunk on their wedding night.
RAIDERS OF THE LOST ARK has another excellent example. Indiana Jones is chasing after the men who have kidnapped his girl, and a huge bad guy with an enormous sword steps in front of him. The expectation is that Indie will pull out his sword, and they will fight.
Instead, pragmatic Indie pulls out his gun and shoots the man so he can continue after the girl. The big fight trope is not only skewered, but also the viewer realizes that Indie doesn't buy into the heroic yet stupid belief that a fight must be between equals with equal weapons no matter what the cost. For Indie, the girl's life is more important than the heroic ideal of an equal fight.
One of the most important things to remember about using a story twist is that the story itself must hold together and have depth of character and plot without the plot twist. The twist is the cherry on top of the sundae, not the sundae itself.
The other thing to remember is that you have to play fair with the reader and give them bits of information that will give them little clues to the big twist. It shouldn't appear arbitrary or come from thin air.
If Bruce Willis' ghost character interacted with live people as well as with the little boy, the viewer would have felt cheated. Instead, they think back to him talking to a wife who is ignoring him, not because their marriage is in trouble, but because he is dead, and she can't see him, and the viewer will gasp with surprise and wince at missing all those clues to what was really happening.
If you can make the reader gasp with surprise and rethink what she's read, your twist has worked.