I see why you are confused.
You can only connect to the local ethernet with either the rj45 or the aui interface. Not both. Depending on the software, the router will default to one of the connectors, and so you may have to specify which connector to use in the config. (It probably will default to the rj45 ethernet port.)
The description for the serial interface on the cisco web is:"Connects the router to 56-kbps and dataphone digital service (DDS) through an integrated 56-kbps DSU/CSU."
I guess this interface can then be used to connect to some form of isdn network or simular. Seems to be an american standard, so I don't know much about it.
Hope this helped you a bit at least.
best regards
katamann@hotmail.com