eD2k is a command included with the aMule application in order to allow starting new downloads from the command line.
It is also commonly used to handle ed2k:// links from the web browser.
It's usage is as follows:
The double-quotes (") have to be used so that the command-line interpreter doesn't resolve the special characters like the pipe character (|), the ampersand character (&) and such, so that it doesn't handle them as commands themselves.
The ed2k command doesn't communicate with aMule through the External Connections interface. Instead, it communicates through the ED2KLinks file.