Basiclly the Transmit (TxData) wires send data from the computer to the rest of the network and the Receive (RxData) wires receive data from the network. The Tx- and Tx+ signals are known as a differential signal pair. An integrated chip on the network adapter combines the 2 signals back together for the receive and vice versa for transmit.
The advantage of using a differential signal pair is the signal can be transmitted over a longer distances then single ended signals and have better noise immunity. RS-232 serial data is an example of a single ended signal.
Ethernet wiring is known as UTP - Unshielded Twisted Pair. Due to the characteristics of a differential signal for most cases a shielded wire is not required. Basically the more twists per inch the faster the data can be transmitted.
The following info is for RS-422 & RS-485 but the basic theory is the same.
http://www.bb-elec.com/tech_articles...ir_signals.asp