Network Port - Also known as a socket. When visualizing TCP/IP network connectivity, it is helpful to think of the computers as having banks of plugs like the old-timey telephone operators used. Just as different residences may be hooked together with the plugs on the operators board, the various programs you have running on your computer are addressed through their numbered sockets - for example, E-Mail is often sent to your e-mail server's port 25, which is always listening for connections. Programs seldom, if ever, share ports, and some programs can use multiple ports. Click here, click "Proceed," then click "All Ports" to find out which ports you have listening.
The first 1024 ports have been reserved for "well-known services." The rest are generally up for grabs, although most popular programs use well-known upper port numbers - for instance, Windows Remote Desktop typically uses port 3389, but can be told to use any port through a simple registry hack.
"Listening" ports (open ports) indicate that a computer is providing a service on the network - thus "listening" for a connection. While not all network services are bad, and many are required for the proper operation of home and business networks, having a port listening on the Internet is really bad if it is unintentional - the services listening on the open ports may be exploited by worms or malicious hackers.
Server - Any computer offering services on a network is called a server by us geeks. However, a server to you office pros is the central computer that holds all your goodies while you're not working on them. For my typical customer, an office server not only stores and backs up files, but also serves the "Intranet" e-mail, calendar, and other, more essential services like authorization, authentication, and event logging.
TCP/IP - Transmission Control Protocol/Internet Protocol is a suite of networking protocols (languages) upon which the Internet, and more recently our office networks, heavily rely. It doesn't matter if you're running Windows, Linux, or Mac OS X, if you use the Internet, you use TCP/IP. When you "ping" someone, you are using the most basic parts of the TCP/IP protocol.