A network interface card (herein
NIC) is a networking device that you install in a computer (or printer,
PDA, etc) that allows you to connect to a network.
Back in the day NICs were actually two cards, a
transceiver to send and recieve data and another card (can't think of the name) to do everything else; but nowadays they're combined into one card. Because of this NICs are considered a Layer 1
and Layer 2 device by the
OSI Reference Model, with the transceiver being the layer 1 device. Your NIC has a unique identification number known as a
MAC Address burnt into it by the manufacturer, which is required to be on any network.
NICs have different transceivers for the type of cable you'll use to connect to your network: RJ-45 for twisted pair, BNC for Coax, FDDI for fiber-optic, etc.
Thanks to lj for correcting some of my info.