Hostile Mystery Eggs are, like the normal Mystery Eggs, a way to obtain spawn eggs. Simply hold the egg in your hand, right click and a random "Hostile" spawn egg will appear. Hostile beeing mobs that attack you, like Zombies, Skeletons, Creepers etc.
To obtain a Hostile Mystery Egg, you will need to craft it. It will need the normal mystery egg as well as some vault diamonds, vault essence and vault meat, all of these are obtained within the Vaults.