Each Realm is a copy of the Live game of Wizard101, and you can change Realms easily, if you want to meet up with friends, find a quieter area or if you're looking for a more populated Realm with lots of people to help out.
To change Realms, simply press your ESC key while you're not in a duel, and you will see a tab on the right that has two little blue globes on it. Click this tab and you will see the Realms page open up. From here you can select from the long list of Realms by clicking on a Realm that is not Closed, and pressing the "Go to Realm" button. You will be teleported to that Realm, in the exact same spot you were standing in your previous location. There is a countdown between Realm changes, so if you're teleporting to friends, make sure you pick the right one!
Note that when the game has to pick a new server for a character (either a new character, or the character's previous server is full) it puts new characters onto the earliest server alphabetically with room. I'm not sure of the exact threshold for this; possibly less than "crowded". It rarely sticks players by default on anything later than Dworgyn alphabetically. The early servers alphabetically are reliably busy except at way off peak times, while the later servers are reliably pretty thinly populated. Ones in the middle like Diego and Drake vary wildly by time of day.
As such, a selection of a server is mainly a choice of how crowded you want for it to be. Note also that on the later servers, the only people there are the ones who manually switched to it; I expect that this would be somewhat correlated with more computer-savvy people.
Note that unlike a lot of games, transferring between servers is quick and easy. No need to wait for the company to manually transfer you, let alone for you to pay a server transfer fee. If one server is acting up one day, it's easy to get off it.
One reason why this is possible is that you don't have to have a unique name, so it doesn't matter if there's already someone on another server with your name. There are quite a few "Luke SkyWalker" characters, for example.
