The unicorn didn't actually appear in the original theatrical release of the movie; it only appeared in later versions, like 2007's The Final Cut. All we see in the original is the origami unicorn that Gaff leaves for Deckard to find at the end of the movie. This kind of ruins the whole point of the unicorn symbolism though, as it was first intended, and it apparently wasn't Scott's intention to cut it from the theatrical release.

So, in case you didn't see one of the later cuts, allow us to explain: in the middle of the movie, Deckard gets drunk and looks at family pictures while sitting by the piano in his apartment. In the original theatrical cut, that's all that happens. But the later versions reveal that there was actually a brief dream sequence at this moment, in which Deckard sees a running unicorn.

The fact that Gaff then leaves behind a silver origami unicorn is meant to the indicate that he knows Deckard's dreams… indicating that those dreams were perhaps implanted, just like Rachael's memories… which would mean that Deckard may actually be a replicant.

That's what Ridley Scott himself said he intended—though one of the screenwriters, Hampton Fancher, said he wanted it to be more ambiguous. On the other hand, Harrison Ford said that he portrayed Deckard with the belief that Deckard was a human, which kind of throws a small wrench into this discussion. (Source)

Also, earlier in the movie, when Deckard is trying to refuse his new assignment, Gaff sets down an origami chicken, indicating that he's too chicken to accept the quest. Sure, that's as deep as the unicorn, but we thought it was worth mentioning.