When Stanley passes by The Fern, the Narrator will tell him to go back in to the room and analyze it, because it "will be important later in the story" and to "make sure he studies it closely, and remembers it carefully." The importance of The Fern is disputed, as it has little to no importance storywise so far. It does reappear during the Baby Game 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.