Filemaker Pro, Filemaker Advanced, and Filemaker Server Advanced have a simple web server builtin.
When you turn Instant Web Publishing on, the web server is activated.
If you have a database open and set to be iWP'ed, FMP calculates the webpages needed to display the database in a browser.
When you turn on IWP the default Port address is 80 - this is the default port for almost all web servers.
Port 591 is the port defined as a Filemaker IWP port by those that decide those things.
This means that any computer on your LAN (Local Area Network - http://en.wikipedia.org/wiki/Local_area_network) can access the database.
The IP address in the turn on IWP in filemaker will likely be a 192.168.xxx.xxx IP address - this is your local IP address on your LAN.
If someone outside your network types your LAN IP address in a browser, they will get an error or connect to a computer on THEIR LAN.
http://whatismyipaddress.com will tell you what your WAN (wide area network - the www) IP Address is.
Your computer does not care what that WAN IP Address is, your router and / or ISP cable / DSL box take care of connections to the internet.
If someone types http://yourWANIPaddress:591, the request goes to your ISP box andor router.
The router has to be told which computer to send the FMP IWP request to, even if only one computer is on the LAN.
http://portforward.com has instructions for most routers to setup portforwarding.
TEST 1 - IF you have FMP running AND IWP is turned on (with Port 80), you can test it by entering http://127.0.0.1 in a browser.
This is a local loopback IP address and will connect to your computer. http://en.wikipedia.org/wiki/Localhost
If you do not have a database open and set to view with IWP, there will be no databases to select in the IWP login page displayed.
TEST 3 - go to a computer outside your LAN and enter http://yourWANIPAddress or http://yourWANIPAddress:591
Google "IWP site:forums.filemaker.com" IWP threads in these forums
This video from MightyData's 11 Days of FileMaker 11 shows the new Instant Web Publishing interface in FileMaker Pro 11.