http://en.wikipedia.org/wiki/Homeplug (Powerline , aka HomePlug)
http://en.wikipedia.org/wiki/Multimedia_over_Coax_Alliance (MoCA)
These are two alternatives to running a long ethernet cable between the router and XBOX. Powerline use your home's internal power lines, whereas MoCA use your home's coaxial lines (the stuff that distributes satellite/cable TV throughout your home). They're bridging mechanisms between your router and the XBOX.
You can buy these as "kits", placing one adapter near the router, the other near the xbox, and running ethernet cable from the adapters to your devices.
[router]<-- wire -->
[powerline adapter #1]<-- internal power lines -->[powerline adapter #2]<-- wire -->[xbox]
[router]<-- wire -->
[moca adapter #1]<-- internal coaxial lines -->[moca adapter #2]<-- wire -->[xbox]
IOW, what’s in
BOLD is a replacement for what would normally require a long ethernet cable. You’re just leveraging other types of wiring you may already have running throughout your home to connect the router to the XBOX.
Of course, there’s no guarantee these will work any better than a wireless adapter on the XBOX. They have limitations too. Sometimes powerline adapters don’t work at all, or poorly, due to local wiring issues. Sometimes MoCA adapters don’t work because they typically can't coexist w/ satellite TV systems (cable systems are OK). MoCA solutions are typically MUCH faster, more reliable, and more consistent than powerline solutions, but they're more expensive too. Sometimes only one or the other solution works at all, leaving you only the other option.
So (assuming wireless remains out of the picture), it’s either powerline or MoCA, or else running ethernet wire across the floor or pulling it through the walls. The use of powerline/MoCA is an attempt to prevent the need for these otherwise draconian measures.