ethernet is a cable, connecting your pc and other pc`s you have in your home, to each other and the router you use to connect to the internet. It connects your LAN, your Local Area Network.
its a hard wire connection, point to point.
Its often more reliable than wireless connections,but limited by distance..the length of the wires..:)
its more secure than wireless, because no one except those connected using the wires can access it.. unlike wireless connections that can be (accidently or deviously) monitored and used unknowingly.
i use the ethernet to connect my pc`s to my BT router,because my wireless connection sometimes lost range, it wasnt stable enough. Also, it constantly picked up neighbour wireless LAN`s and i did not like that possible insecurity.. if i could see them, they could see me...so could anyone, now they cant.
The downside of using the ethernet instead of a wireless connection is having to route the cables through your house.. and if you only have ethernet cables and no wireless.. you cant just walk down the garden and link to your LAN using your laptop wireless... its about choice really.. and suitability.. if you need to be totally mobile .. use wireless, if not, use ethernet.. or somewhere between... use both.. :)