The elixir puts your character to sleep and creates a Dream Vision version. Use an Elixir Master alchemist if you want to try for the biggest bang for your supply of materials.
Extremely useful for grabbing screenshots of mobs in their natural environment. :) It's also great for checking for rare mobs in instances without having to clear as many mobs. Handy for Horde characters (working on the Universal Explorer achievement) with no stealth capabilities to get past the draenei guards protecting the Draenei starting zone... or enter the other faction's area in Dalaran (applies for Alliance characters, too).