Tethering - definition
In the context of GSM mobile phones, tethering describes the process of connecting a phone to a computer so that the computer can access the internet via an EDGE/UMTS/HSDPA network. In this way, the mobile phone acts as a modem for the computer.
That specific use of the word "tethering" stems from the fact that to be used as a modem, the mobile phone usually has to be connected to the computer via a USB data cable. In recent years however the same thing has become possible without cables by using a Bluetooth connection.
Thus, tethering has turned into a generic term for using your mobile phone as a GSM modem for your computer.
Some carriers require that you sign up for special plans in order to use your phone for tethering, while for others it's simply a matter of paying the data traffic used, much like you pay for browsing on your mobile phone.