Deleting a character is rather straight forward:
2) Select a character from the list and click the "delete character" button at the bottom of the screen.
3) A dialogue box will appear to confirm your character deletion.
4) Type "DELETE" in the box and click "Okay".
There are quite a number of videos on youtube that parade the deletion process. See some of them here.
However. Deletion does not guarantee erasure of the database and servers of World of Warcraft. In fact, Blizzard, the makers of WoW, have a policy that permits restoration within three days of deletion. I like how they describe it as a reunion. Cute.
src: Character and Item Restoration Policy, December, 2010 [masked for emphasis]
According to WoW forums and wikis, players seem acutely aware that they are playing on servers and that their characters are produced and stored within a database. Blizzard names their servers and/or datacenters realms. Since game play relies on low network latency and high server response times, selection of a fast realm, usually the closest, is perceived as a critical factor in play. Users track the physical locations and Blizzard reports the status of their servers. In addition, users report that Blizzard's WoW Game Masters are willing (and perhaps able) to restore characters depending on that character's ranking in the game and that restoration may take place much longer after 3 days.
With all its wizardry, virtual property, mages, and talk of magical realms, WoW players may have a more acute awareness of the materiality of their online exchanges than corporate users on Microsoft Exchange.