When you use a web browser's address bar to find a web page, you might type something like "http://www.myfavoritewebsite.com". The "www.myfavoritewebsite.com" part is called a domain name. Alternatively, you can use an Internet Protocol (IP) address, such as 10.102.2.2, to find a web page. Browsers will accept this as an address (try http://10.102.2.2), and in fact web browsers use a Domain Name Service (DNS) to "translate" a domain name into an IP address. A domain name can point to a wide range of IP addresses (around 4 x 109). There are rules regarding the format of valid domain names, with the result that there are about 2.5 x 10396 valid, unique domain names. Since new web sites are being set up every day and new devices (which also require unique IP addresses) are attaching to the Internet every day there will be a shortage of IP addresses long before there is a shortage of domain names. This is expected to occur sometime in 2012.
Perhaps the Mayans were right.