What is a port?

In TCP/IP* and UDP* networks, (a port is) an endpoint to a logical connection. The port number identifies what type of port it is. For example, port 80 is used for HTTP traffic.
http://www.webopedia.com/TERM/p/port.html

Well Known TCP Port Numbers

http://webopedia.internet.com/quick_ref/portnumbers.asp

Web-Based open port scanning

Use 'Shields Up' at http://www.grc.com

App-Based open port scanning

Several network freebies include this. LanSpy looks worth a try.

How do you close an open port?

Stop the service which has it open, or configure your firewall to block it.
http://www.emsisoft.com/en/kb/articles/tec021114/


*
"The TCP protocol is often used when reliability is more important than speed, since constantly acknowledging the other computer can slow down communication. That’s why sending email or transferring files is usually done using TCP.

The UDP protocol is most often used for streaming video or Internet telephony where speed is more crucial. The UDP protocol saves time because it doesn’t go through the "handshaking" process that the TCP protocol requires, but like TCP, UDP can still be 100 exploited."

http://www.windowsitlibrary.com/Content/1845/08/1.html#1