Being one of the most multi-sided terms on the Internet, 'host' can be used in a variety of contexts.
Network Host
From a networking point of view, a 'host' refers to any computer (server) that is interlinked with another machine(s) through an Internet connection. Each host has its unique IP address, formed by the computer's local number and the particular number of the network it belongs to. The Internet host in this case is responsible for storing data that will be transmitted to other machines, usually users' computers, called remote terminals.
Another networking use of 'host' is when the Point-to-Point Protocol (aka PPP) is adopted for executing a connection between a user's computer and his/her Internet provider. In this case the user is assigned a unique IP address for the time the Internet connection is being carried out, where the user's computer acts as a host for that connection, which is actually a networking node.
Web Host
In the language of web hosting, a 'host' refers to a web server that stores website files, as well as various programs and applications. In this light, a 'host' refers to the bundle of hardware, software and communication lines required for the hosting service to run smoothly.
To take advantage of this commercial use of 'host', website owners, individuals or companies need to sign up with a web hosting provider and choose a plan that corresponds to their particular demands. They will be able to connect to their particular host to make various file manipulation actions either via an in-built File Manager, or via FTP access provided by the hosting provider, whereby the client's FTP software connects to the provider's FTP host server using an FTP connection. Very often, you could find the web hosting company itself to be referred to as a 'host' for the sake of brevity.
Other Uses of 'Host'
In the field of mainframe computer environments, a 'host' represents a mainframe computer that provides host services to certain workstations. In this context, a 'host' is also known as a large server to the Internet audience.
In more general terms, the 'host' term is usually attached to a powerful device or program that delivers services to some smaller and less capable device(s) or program(s).