An alliance is quiet simply, a group of people (though many one person alliances exist) that are united as a way of having a bit of a protection buff. It doesn't actually give you any bonus, but it can steer away some would be attackers, depending on the number of people in your alliance and their might. If you get attacked by someone in a small alliance or a lone wolf, your alliance will usually go in and take him/her out. However, if someone is in a large alliance or group of allied alliances, they will mail the other alliance leader asking them to stop stop that person from attacking, or just leave you on your own. Alliances will get into wars though, and if you are a low level just seeking protection, you will probably get swamped by the enemy alliance members.
Joining an Alliance Edit
It's not all that complicated to apply
Step 1. Go to the icon at the bottom if the screen that says Alliances, and click it.
Step 2. After you are in you will see two lines. Click the one that says "Join an Alliance."
Step 3. Type in the name of the alliance you wish to join.(Note: Some alliances have requirements, usually involving might, so you may not get in. Each alliance also has a max of 100 people.
Step 5. The Leader of the alliance will get a request in his embassy. When he goes and looks, he can either accept you, or reject you.
Now your in or rejected. If your in good job, get out there and start owning noobs. If you were rejected, keep trying I guess.