When you pass by the Fern, the Narrator will tell you to go back in to the room and analyze it, because it "will be important later in the story" and to "make sure you study it closely, and remember it carefully." The importance of the Fern is disputed, as it has little to no importance storywise so far. It does reappear during the Art Ending though.
The Raphael Parable
The Fern reappears in The Raphael Parable. It is the key to finding one of the 34 secrets, which must be attained by staring at it.