What is Dark Elixir?

Solution 1:

The Dark Elixir storage is where Dark elixir is stored and is similar to Elixir and Gold storage buildings. Dark Elixir is used to train Dark Elixir Troops through the Dark Barracks, as well as buy and upgrade Heroes.

Dark Elixir Troops are extremely expensive to train (because of the rarity of Dark Elixir), but are also generally more powerful than normal troops. Dark Elixir troops reside in the Army Camp, similar to normal troops e.g. Barbarian, archer etc.

Heroes are super powerful troops that do a lot of damage. They are immortal, but if injured in battle must sleep to regenerate their health. There are two heroes, the Barbarian King and the Archer Queen.

You can acquire Dark Elixir from raiding, or with the Dark Elixir Drill which is first unlocked at town hall 7 and a second one at town hall 8.

As of the Dark Spell Factory Update (1/7/15), Dark Elixir can also be spent on Dark Spells which are simpler spells which although are more specialized, are more powerful (compared power-per-storage-space to their elixir counterparts) and take up less space.

Solution 2:

Dark Elixir is a more powerful and rare form of elixir. According to the Clash of Clans Wiki:

Dark Elixir is a resource that is collected by dark elixir drills. Once collected it is stored in your dark elixir storage. The amount of dark elixir you have is displayed at the top right side of the screen under elixir. Dark elixir is used for purchasing and upgrading hero class troops, as well as training and upgrading dark elixir troops.

Dark Elixir is created/found with a Dark Elixir Drill. They can be obtained once you reach Town Hall Level 7. Mining Dark Elixir takes time, because it IS rare.

Dark Elixir can buy you several troops, which include minions, Hog riders, Valkyrie, and others.