As you may know, internet domain names (like website.com) could be rented (registered) for some fee for some period of time, from one year to 10 years. You can choose any name that isn't taken yet with various "suffixes" (.com, .net, .org or .co.uk, .de and so on).

That "suffixes" is called TLDs - Top Level Domains. Some of them are generic, like .com for commercial websites, .net for network related projects, and the others are national like .uk for United Kingdom or .de for Germany.

Though there is no centralized government in the internet, some organizations are needed to make internet works. One of that organization, and the most important one, is ICANN - Internet Corporation for Assigned Names and Numbers. Created in 1998 ICANN non-profit organization overseeing internet domain names, generic top level domains and IP-addresses.

But you needn't (and you can't , actually) contact ICANN directly to register your own domain name. Instead you should contact ICANN accredited registrar - commercial company that is approved by ICANN to resell domain names. You can choose any accredited registrar since all of them have been checked up by ICANN. Also you can transfer your domain name easily from one registrar to another if the former doesn't suit you anymore for some reasons.