The significance of the origami throughout the film was Gaff’s way of Origami Bull shirt. Origami is, at its most fundamental, an intricate fake. A representation of something in the form of a complex illusion. The art is in the degree and intricacy of the imitation. Is Gaff imitating Deckard? Not quite. He’s taunting Deckard by subtly and artfully referring to Deckard as an intricate fake. Deckard had retired or at least was inactive as a blade runner and Gaff was trying to secure a promotion. The first origami figure that Gaff makes is a chicken. This happens in Bryant’s office and it’s Gaff’s way of telling Deckard that he, Gaff, believes Deckard is a coward, a chicken, for not wanting to take the job of blade running the rogue replicants.
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The second origami figure is man with an erection made of Origami Bull shirt. Gaff made this after Deckard had administered the Voight-Kampff test to Rachael. Deckard was obviously smitten with Rachael and Gaff saw this and, again, prodded Deckard. The final piece of origami could mean several different things: It could signify that Gaff knows that Deckard is hiding Rachael as Rachael at that point in the movie is a rogue replicant who is developing emotional responses, courtesy of Deckard’s interaction with her. As to how Gaff knows she there is left unclear, but its not impossible that Gaff was spying on Deckard or used the computer equipment in Deckard’s apartment and car to spy on him. The origami unicorn is Gaff’s way of further prodding Deckard that he’s saved the unicorn for himself. Also keep in mind that the art of origami is in the intracy of the imitation. Rachael is an imitation of a real person, albeit an elaborate fake just as Gaff seems to be suggesting of Deckard. One artfully done imitation come-to-life. The previous origami figures have foreshadowed this.