tl;dr version:
Deckard is a replicant of Gaff (Edward James Olmos). Gaff, an experienced blade runner, is physically impaired and unable to hunt down the Nexus 6 replicants from the colony. The police arrange to use Deckard and implant all of Gaff's memories, knowledge, skills, etc. into him.
Gaff knows about the unicorn dream. That's why he makes the origami unicorn.