Strongholds are small, mini-servers that cover a very small portion of the full map, where the player can do whatever they want.
 Where can I rent Stronghold servers?
First off, if you pre-ordered either the Pioneer or Legend packages, you will get a stronghold server. Pioneers will be given a 1 month Server where else the Legend package gets a 6 month server.
Clicking on PLAY GAME will provide two buttons - MY SERVERS and MY STRONGHOLDS. On the My Strongholds screen you'll see all available stronghold maps. There you will be able to choose a map, the duration ( 1,3,6,12 months ) and number of slots ( 15,30,45 ).
Currently as of Alpha Testing (October 15-13) Stronghold servers have not yet been enabled.
 What are these maps?
These maps are typically around 3-4 square kilometers in size with 1-2 "settlements" per map that act as a home base for either a single player or a group of players. The zombies spawn on the outskirts of the map, but can be lured into the settlement.
 Are there loot on these maps?
There are very few loot spawn locations, and is slightly different from what you'd expect on main gameworld maps. Very basic food items and some unique "building" materials "local" to this stronghold map will be found on these servers. "We want to encourage players that runs different stronghold maps to barter with other players, exchanging building "blocks" that can be used to modify your map."
 So, what do I do with these servers?
If you want a simple answer, anything. This can range from creating a sort of "safe haven" for friendly players to roleplay on or to a farm that provides food that you can sell to fellow players, it's all just up to your imagination and building blocks.
 How much does renting a Stronghold server cost?
Stronghold servers will cost $5 per month. Sergey commented here in Russian that with the legendary pack, you get "30 bucks in the form of game currency + $ 30 in the form of hosting your own server...".