Forgive me for a little bit of pedantry: The home wireless networking that you're talking about is in fact an Ethernet technology. The difference between wired Ethernet and wireless Ethernet is (as others have stated) about speed, security, and convenience. For home users, wired Ethernet is faster and more secure (assuming that you prevent unauthorized users from plugging into your network equipment) but significantly less convenient for some.

Typically, speed of home wireless networks is so much less than the Internet connection speed that going to wired Ethernet isn't helpful. The big exception is if you have significant traffic that's going between devices on your network (not Internet traffic). In that case the increase in speed locally can be very worthwhile.

I found that streaming video (Netflix) didn't work well via the wireless connection to my DVD player, but when I went to the trouble to install wired Ethernet the problems were resolved. Otherwise I use wireless at home.