TCP/IP stands for Transmission Control Protocol / Internet Protocol and it is the protocol / standard that makes the Internet work.
Overview: When your computer (can be called a 'host') wants to communicate with another computer on the Internet (another host), your computer sends IP Packets out to the Internet (like through your modem) addressed to the IP Address of the destination computer. Every computer connected to the Internet has an IP Address. Routers in the Internet that are interconnected to each other understand how to examine this IP Address information and foward the IP Packet to the next appropriate router that will get the IP packet closer to its destination. This forwarding of the IP packet is repeated until the IP packet reaches its destination.
IP Address: An IP address is just four numbers, each in the range of 0 to 255, separated by periods. For example, 18.104.22.168 is the IP Address of our VisualRoute server. An IP Address is like a postal address that identifies a building.
IP Packet: A piece of information (such as part of a web page) with 'to' and 'from' IP Address and Port Number information, and other miscellaneous infromation, such as TTL, etc.
Port Number: A number from 0 to 65535. A port number helps to distinguish one program communicating accross the Internet on your computer from another program. A port number at an IP address is like a named person at a postal address / building.
TTL: Time To Live. It is an integer value between 0 and 255. Each time a Router fowards an IP Packet, the TTL value in the IP Packet is decremented by one. When TTL gets to zero, the Router discards the IP Packet and an ICMP 'TTL Expired in transit' message is sent back to the sending IP Address. This mechanism prevents an IP Packet from being routed around the Internet forever, if for some reason there is a routing loop that would just send the packet around in circles.
Router: A router is a device that, when interconnected to other routers, can receive IP Packets and foward them to other routers that are closer to the desintation IP Address in the IP Packet.
Hop: Each time that an IP Packet moves one step through the Internet, that is considered a hop.
ICMP: Internet Control Message Protocol. ICMP is the control and error reporting protocol for IP. For example, when the TTL field of an IP Packet reaches zero, a Router will send an ICMP 'TTL expired in transit' message back to the sending IP Address.
For a detailed technical discussion of TCP/IP, read RFC 1180, A TCP/IP Tutorial.