In The Prestige, what is the meaning of the phrase "the pledge, the turn, and the prestige?"
Christopher Priest wrote The Prestige in 1995, and it was met with critical acclaim; director Christopher Nolan adapted it to film and similar critical acclaim in 2006.
The novel deals with the inner world of stage magic and magicians; the two protagonists are magicians who become rivals, seeking to outdo each other. The central motif of the novel is the three-part structure of a magic act; this is described differently in the novel than in the film, but the ultimate act is the same. In the novel, it is described as follows:
First there is the setup, in which the nature of what might be attempted is hinted at... the magician will make every possible use of misdirection.
The performance is where the magician's lifetime of practice... produce[s] the magical display.
The third stage is sometimes called the effect, or the prestige, and this is the product of magic. If a rabbit is pulled from a hat, the rabbit, which apparently did not exist before the trick was performed, can be said to be the prestige of that trick.
(Priest, The Prestige, Google Books)
In the film, it is described more poetically as "the pledge" (setup), "the turn" (performance), and "the prestige." This allows the film to follow the structure of the magic act itself, showing first the setting and characters, then their actions as they try to best each other at magic, and finally their resolution as one performs "the prestige" and everything is revealed to the audience. The novel does not follow this structure as firmly, since it is presented as the reading of letters by a modern-day descendant, but it uses many of the same motifs to show how the jealousy and pride of the two magicians serve as catalysts for their actions.
In either case, the three-part structure of magic serves to showcase the use of misdirection and public showmanship in the telling of a story. The dueling magicians each use performance to attack the other, and each has a moment of "prestige," where their inner plotting is revealed and the "magical" act or result is shown.