Summoning and defeating Anzu is the final step in the druid epic flight form quest line. Once the quest line is completed, the druid will receive another moonstone that can be used in future runs through heroic Sethekk Halls. Only druids can use the key.
Note that the moonstone is treated as a key and is therefore stored in your keyring.
The process to summon Anzu was removed in Patch 4.0.1, he's now a regular boss. This renders the Essence-Infused Moonstone pretty much useless.