External Connections
Note: Since there's no info at all about this, I'll write what I think External Connections are. I'm no expert so I may be wrong, so take the following with a grain of salt. If some experts thinks this info is right, then please remove this comment (and if it's not, please correct it and remove the comment anyway! ;-) ).
External connections are the way aMule has to communicate with external utilities, like the webserver. So, when an user is controlling aMule remotely with a web browser, he's not talking directly with aMule, but with another program (amuleweb in this case) that is who really listens at port 4711. This program then talks with aMule using the external connections mechanism.
Since usually both aMule and their utilities run on the same machine, there's no need to redirect the external connections port in a firewalled environment (NAT network with a router, etc.).