Space Honey, also known as Royal Honey, is a type of honey made by the Space Bee. It is hazardous to eat because of the strong effect it has, which causes people to enter a deep state of sleep that would leave the person in a comatose state if they ingest too much.
Professor Farnsworth sent the Planet Express crew on a mission to retrieve samples of the honey, which was supposedly a mission in which all of the previous Planet Express employees had died trying to accomplish. Bender, Fry and Leela had barely escaped with the Queen Bee nearly destroying the ship.
As told by Zoidberg in "The Sting", a single spoonful of the honey will calm you down, the second spoonful will cause you to fall asleep, and eating a third spoonful will put you into a state of sleep so deep, you will never be able to wake up.
Leela starts using the honey anyways to help her fall asleep. In one of her dreams, she accidentally spills the honey onto the sofa and creates an exact duplicate of Fry after he died during the mission (Fry only died in Leela's dream). It was explained that remnants of Fry's hair and skin from the part of the couch where he would always sit, had mixed with the honey and replicated his entire being. This was in a dream though so it is unlikely that the honey actually does this, nor is it likely to put the consumer into a deep sleep.