It means that the writer, movie, or speaker presented something very unexpected or surprising. An example could be when the hero's partner is shown to be the villain, or when the characters are revealed to have been on a different planet for the story. (By any chance, did you maybe see this on Robot Chicken in the episode when they were joking about M. Night Shyamalan?)

O puedes llevarlo también acompañado a tu léxico en una frase, es decir: wow que giro dio el profesor de matemáticas con esa ecuación de álgebra

That something unexpected happened, usually at the end of a film or book. Everything was going well, the couple were ready to get married and the bride arrived at the church. However, the groom had run away with her best friend. What a twist!