This model was successful because it delivered such basic services as file transfer, electronic mail, remote logon - services everyone needs. Several computers in one department can use TCP/IP on a single LAN. The IP component provides routing from the department to the enterprise network, then to regional networks, and then to global Internet.
TCP/IP is a two-layer protocol. The upper layer - Transmission Control Protocol - assembles a message or file into smaller packets transmitted over the Internet and received by a TCP layer that reassembles these packets into their originals. The lower layer - Internet Protocol - manages the address part of each packet and controls that it reaches the correct destination. Every gateway computer on the network checks this address in order to forward the message (file) to its destination. Some packets of the same message are routed differently, but they are reassembled at the destination.
TCP/IP uses client/server communication model. In this model a computer user (client) requests a service (sending a webpage) and is provided with it by another computer (server) on the network.
We all know even higher layer application protocols that use TCP/IP to get to the Internet. They include Hypertext Transfer Protocol (HTTP), File Transfer Protocol (FTP), Telnet, and the Simple Mail Transfer Protocol (SMTP). These and other protocols are often packaged with the TCP/IP as a suite.