The dream potion is used in both the Dream Mentor and Dragon Slayer II quests. The Oneiromancer tells the player that the potion will send them to the Dream World to attempt to combat either Cyrisus' fears, or Bob the cat's past. The potion puts the player in the NPC's dream and binds the two subconsciouses together.
With the two minds melded as one, the Oneiromancer says both characters need each other to survive. If one dies, both die, "just as if you were killed by a monster in the wild", the Oneiromancer cautions.
During the Dream Mentor quest, you give the Dream potion to Cyrisus, who puts it on the brazier used in the Lunar Diplomacy quest. You then light the burner and are transported to Cyrisus's dream, where you have to conquer his fear of combat by fighting four monsters: The Inadequacy, The Everlasting, The Untouchable and The Illusive.
During Dragon Slayer II quest, you must first light the brazier, then add the potion onto the flaming pyre. You will be in a different dream world, where you must defeat Robert the Strong in combat.
Warning: If you die while carrying the Dream potion, it is lost and you will need to create a new one.