You may apply for a Mystery Egg once a month! Mystery Eggs are special eggs that hold a randomly chosen Pokemon. They could be anything, and they also have the chance to be shiny! Mystery Eggs have a better chance of being shiny rather than just entering the shiny raffle with a regular egg. (Instead of a 1 in 8192 chance, there's a 1 in a 4096 chance!)
To apply for one, you can apply under the Pokemon Egg - Applications. This is a lot of fun, you never know what you're going to get. It may be something very interesting.
It also adds a very nice spin to your team. It adds diversity. If you have any questions about this, or you would like a farther in depth explanation, please ask myself, Reiici, or another admin.