This week's book giveaway is in the OCAJP forum. We're giving away four copies of OCA Java SE 8 Programmer I Study Guide 1Z0-808 and have Jeanne Boyarsky & Scott Selikoff on-line! See this thread for details.
80 is used for non-secure (http://) connections.
443 is used for secure (https://) connections.
By default Tomcat is configured to run on ports 8080 and 8443.
There are a couple of reasons for this.
1.) Tomcat, in its early days was almost always run behind another web server like Apache HTTPD which would already be bound to ports 80 and 443
2.) On *nix machines only applications started by the root user can bind to ports under 1025 and application servers shouldn't be run as root
If you want to run Tomcat on the default ports on a windows box, simply edit server.xml.
Look for the <Connector ... /> entries and you will find the port attributes.