But actually 'web' reveals to the graph of hyperlinks between http/html pages that let you navigate from page to page, server to server. www denotes the host is primarily a http server serving web pages.
You could argue it's superfluous these days - if you are typing it in an address bar, you hope it is a http server, and if you are typing it in a ssh prompt, you know it's your ssh server. People add it because it's a convention and some users might get confused if you don't... (it's probably a vhost anyway most of the time)