To begin with, there are three main regions recognized by the game: North America, Europe, and Other. Digital versions of the game are automatically entered into the correct region based on the purchaser's location, while physical retailers give out a serial code to register in account creation. Players must register a code that matches their location (a customer in Europe has to register a European code), but after that one-time check, they can access the game from anywhere in the world.
Home worlds are automatically displayed by region, but players can opt to join the servers of another region. Once a home world has been chosen, all characters on an account belong to that server, and a gem transaction has to be made to switch to a new home world. That won't be implemented at launch, however, in order to facilitate the spread of a stable and healthy population across all servers. At launch, transfers between worlds will be free. After the populations have settled, world transfers will be restricted to a once per week and cost gems. At the same time, the guesting feature that allows players to visit their friends' worlds will be implemented.
Check out the news post for all the gory details, or hit up the Guild Wars 2 knowledge base if you've got some burning tangential questions.