The River of Forgetfulness is a river in the Land of the Dead with magic water that causes memory loss upon consumption. In "Death in Bloom," the Talking Skull was telling Jake to drink the water after Jake said how thirsty he was. Finn quickly told Jake not to drink the water because the skull wanted him to, but the skull then told Jake to not drink it, so Jake jumped into the river and drank from it. Upon rising out of the river, Jake was overcome with amnesia, hence the name "River of Forgetfulness." Peppermint Butler most likely referenced this river when he said "Don't drink the water" before the portal to the Land of the Dead closed.
The River of Forgetfulness is most likely based on the River Lethe, one of the five rivers of Hades of Greek Mythology. Those who drank from the river Lethe would experience "unmindfulness," which is another way to say complete forgetfulness/amnesia.