You are using the Internet now to read this wiki.
Originally known as ArpaNet, it was created so that in the event of catastrophic communication failure, the US Department of Defence could remotely administer their machinery.
Until the WorldWideWeb came about in 1990, the Internet was almost entirely unknown outside universities and corporate research departments and was accessed mostly via CommandLine interfaces such as Telnet (now Deprecated in favour of SSH) and FTP (now also Deprecated). Since then it has grown to become an almost-ubiquitous aspect of modern information systems, becoming highly commercial and a widely accepted medium for all sort of customer relations such as advertising, brand building, and online sales and services. Its original spirit of cooperation and freedom have, to a great extent, survived this explosive transformation with the result that the vast majority of information available on the Internet is free of charge.
The best known aspects of the Internet are the WorldWideWeb and Email. Other facilities include UseNet, the global 'news' service (largely Deprecated in favour of web based forums and MailingLists, IRC, FileSharing, etc. Anything you can do on a network, you can do (albeit probably slower) on the InterNet.
The internet runs on the TCP/IP protocol, although there are gateways onto it for other networking Protocols. In order to convert IP addresses to names, it offers the DNS. The InterNet is in the process of upgrading from IPv4 to IPv6.
The NetworkEffect ensures that the InterNet is singular. If another internet were built of any considerable size, the benifits of connecting the two internets would grow extreme. Since internets are inherently distributed, sooner or later a NetworkAdministrator would set up a computer so it could access both. For the two internets to be considered a single network only a single, local connection needs to be made, even if it cannot be seen/accessed from the overwhelming majority of either network.
There are debates over what level counts for the InterNet. Given that most users are connected to the InterNet over the POTS and the user-invisible telecoms network (which is usually at least partly digital) I could be argued that every computer connected to a telephone line is part of the InterNet. Data-over-Powerlines networks are usually not considered to be part of the same internet as computers the only supply with power (unless, of course, there's another connection between the two).