Ethernet is a group of similar technologies for LANs (Local Area Networks). It defines standards such as wiring types and signals so that computers and other devices can talk to each other with minimal difficulty.
The most common version uses a twisted pair cable, which typically uses an 8-pin connector (similar to a phone plug, but larger) called RJ45. The cable itself is most commonly Category 5 (Cat5) which itself is most often 4 pairs of copper wires. The number of pins and type of cable is determined by the type of Ethernet, most commonly 10BASE-T, 100BASE-TX, and 1000BASE-T. Ethernet is also available over optical fibers.
Ethernet should not be confused with Internet, though on some level the concepts are similar. With Ethernet, a computer may talk to another computer in your home. The Internet is what is used for your computer to talk to the world. Data from the Internet can enter your home (via a modem). At this point it is sent to your router/hub and to your computer over your Local Area Network, which uses Ethernet.
Conversely, you home could have a Wireless LAN (colloquially, "Wi-Fi) which doesn't have wires, and therefore doesn't need Ethernet. A wireless router would be an example of an Ethernet Bridge, where the router is connected to a modem via Ethernet, but broadcasts a wireless signal for computers and devices in your home.
Ethernet is faster and more secure than current Wireless systems, and in addition to its duties creating a LAN, it can be used to send audio and video over your entire home.
Read HomeTheaterReview.com's article detailing how Silicon Image is preparing HD over Ethernet.