The Local Area Connection is for the network (RJ-45) port on your computer. You may use it in the future for a dsl modem, switch, router, etc.

While in Network Connections, right click the Local Area Connection and select Disable. The icon will not appear in your taskbar anymore. It will still show in Control Panel, Network Connections, but that doesn't matter. It is just showing it as being there, not being used.

You can normally go into the BIOS and disable, along with many other ports your computer has that you don't use, and it won't show at all.
I don't see that this is necessary, as sometimes, later on, people hook up some hardware and can't figure out why it won't work. They forget that months or years ago, they disabled the port.