The World Wide Web is one part of the Internet, and only one form of hypertext or hypermedia. Each of these run on the Internet, which is an international networked computer environment.
Most Internet services relay on a client - server model, and the Web is no different.
When we use the Web we are clients, and the pages we request reside on servers. Servers deliver Web content to us clients. These clients might be you, other readers, even other computers. Different Internet services have different sorts of clients and servers, and different sorts of relations between the client and server. For example in FTP a connection is opened between the client and the server and that connection is maintained - kept open, a bit like when you ring someone up and they answer, the phone line between the two of you is kept open.