"If you got a dead body and you think his brother did it, you're gonna find out you're right."
—Verbal Kint, The Usual Suspects
For example, suppose Alice has been murdered. The only other two people in the house at the time are Bob and Carol. Bob acts mean and surly to the detective, doesn't treat Carol well, and reveals he had both a motive and opportunity to kill Alice. Carol, by contrast, is very polite and helpful, and is visibly upset at Alice's death.
A Genre Savvy viewer would quickly conclude that Carol is the murderer and Bob is innocent. Why? Naturally, the evidence that Bob did it was planted by the author to mislead the audience into drawing a false conclusion. On the other hand, Carol's niceness is seen to be an act to conceal her own guilt.
In many cases, the above description is exactly how it happens (see: most episodes of CSI). However, sometimes the author pulls a fast one - it turns out Bob is guilty after all! All that evidence against him, which the reader dismissed on the grounds of being too obvious, is actually correct and valid. Furthermore, Carol cooperated with the detective because she's that sort of person, and she was genuinely sad that Alice died.
And thus is illustrated the essence of The Untwist. The author drops a large number of hints at the start of the story which a Genre Savvy reader assumes to be obvious Red Herrings, and thus is surprised when, later on, it turns out that the simplest, most obvious explanation was the correct one. Somehow, the author has managed to subvert the reader's expectations by not subverting their expectations, or something. (That is, instead of a Double Subversion, it's a Null Subversion.)
This technique obviously carries with it the risk that if it is not very well done, or the audience isn't very Genre Savvy, they will not anticipate that there will be a twist. If this happens, they will simply go along with what the writer is very obviously leading them to believe, and when the story unfolds that way, they will consider it very predictable and be unimpressed. For instance, in the example used above, they would assume that it was Bob who committed the murder due to the evidence presented against him, and it will turn out to be Bob who did it, which, without the expectation of a twist would be a very boring story.
In most cases, The Untwist is the unintentional result of a writer being heavy-handed with Foreshadowing, such that the reader assumes simple hints are red herrings. It can be done deliberately, but doing it deliberately and well requires a great deal of skill. A common way of doing it deliberately is by playing a Discredited Trope completely straight. Other times, the writer didn't intend the plot point to be a surprise at all - the fans produced an Untwist by expecting a twist where there was none.
Sometimes, though, the heavy foreshadowing leading to a Twist Ending was intentional, but due to circumstances (usually Executive Meddling), the Twist is turned into an Untwist (see the 2007 version of I Am Legend for a good example).
Occasionally played with, e.g. in one fairly famous mystery book, the obvious person is guilty - but the obvious evidence and way he committed the crime is false: It was all part of an Evil Plan based around "double jeopardy" laws which prevent people from being tried for the same crime twice. Basically, he planned to trick the police into using the false evidence at trial, which he would then easily dismiss.
Not to be confused with the German indie/electronic band The Notwist.