A server is a computer that provides data to other computers. It may serve data to computers connected to it, or to other servers. A server can be a computer program, such as a Web server, an FTP server, an email server, or a file server.
A host is a computer that connects to other computers. It may connect to computers in the same room, or to computers in other parts of the world. A host can be a server, or it can be a client. A host can be a computer, or it can be a software program, such as an FTP client, a Web browser, or an email program.