The answer to your question ( and many other questions ) is right in our handy Player Guide. There's a link to the Player Guide at the top of this page.
Realms are copies of the game. Wizard101 has several Realms for our players to enjoy. All the Realms are identical and you can switch between Realms easily when you're not in a duel. Simply press Esc and select the very last tab with the 'two worlds' icon - and you will see a list of Realms to choose from.
CTRL - M is the shortcut key to bring up this section of your journal.
Why switch Realms? Players may choose to switch between Realms that are more or less populated based on their play style.
If you are looking for players to adventure with, you may wish to switch to a Realm with a higher population.
If you are having trouble meeting up with friends or family, make sure you are all meeting up on the same Realm!