The word Port can have 3 definitions in Computer Terms.

The first and most common definition, is a place or input on your computer that information goes into and out of. Examples of this are USB Ports and Parallel Ports.

The second definition is an Internet port. Every service that you connect to on the Internet listen on a particular port. For example, the World Wide Web Service listens on port 80. Whenever you go to a website, your browser is actually connecting to the particular computer on its port 80. Other services use other ports. As another example, when you send mail, you connect to your ISP's mail server on its port 25, which is the SMTP port. Once your computer is connected to the port it sends data to the server over it. If you are still confused you can use the following analogy. Look at a computer on the Internet as a mall and the ports on the computer as the stores in the mall. In order to buy something at the mall you need to enter a store. It is the same way with the Internet; in order to use a particular services at a computer, you need to connect to its port.

The third, and least common used, definition is the translation of a piece of software from one operating system to another. For example a piece of software that was designed to be used on a Macintosh, would have to be ported over to the Windows Operating System before Windows users could use it.

Link: A comprehensive list of port-numbers can be found here.