An Internet host can be a machine or an application connected to the Internet that has an Internet Protocol address (IP address). An IP address is used to uniquely identify every host on the Internet. Because these IP address are unique, they can be used as the source and destination IP addresses in any IP-based communication. At the most basic level, Internet hosts fall into two categories, Servers and Clients. See InetDaemon's tutorial on Client-Server relationships for more information.
Some say that a computer 'hosts' or 'serves' the clients that use an application. This is the orgin of the terms host and server. A host is not neccessarilly a single computer. It is possible for a single computer to use multiple IP addresses, especially when it is providing multiple services such as an e-mail server and a web server at the same time. One IP address will be used to identify the e-mail server software, the other IP address will identify the web server software but both server applications are running at the same time on the same computer. The IP addresses allow each to be accessed individually.
Hosts are organized into groups called Networks. See the next section on Networks for more information.