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.
I have Windows XP on my new computer. If I go to Start/Control Panel/Network Connection, I get icons for my dial-up provider, a New Connection Wizard and a Local Area Connection Wizard. I do not have any other accounts or usernames on my computer. I am the sole account holder. There is no one sharing my computer with me. My Local Area Connection icon is a nuisance. For one thing it puts an icon on my taskbar which I cannot get rid of. I would like to delete the Local Area Connection icon from my Network Connection screen. Can I do this safely? Thank you.