This basically means that the story turns out much different as to that expected. Take for instance Garfield and a plate of food directly in front of him. What would you expect Garfield would do? Normally you would expect him to play with his food and eat it. Instead Garfield grabs the plate of food and gives it to his pet monkey. Garfield doesn't have a pet monkey, I may hear you ask. Well there you have it! Your twist, something totally unexpeted happened in your story. That unexpected outcome is what we call a twist as you can see here. The plot changed drastically from what you would expect.