Tethering, or phone-as-modem (PAM), is the sharing of a mobile device's Internet connection with other connected computers. Connection of a mobile device with other devices can be done over wireless LAN (Wi-Fi), over Bluetooth or by physical connection using a cable, for example through USB.
In the context of cell phones, tethering is connecting your phone to a laptop or similar data device using a data cable, usually for the purpose of connecting to the Internet on the laptop, via the phone's wireless connection to the cell phone network.
Some phones may allow accessing the Internet on the phone itself, but not via tethering.
Carriers usually charge more money for accessing the Internet via tethering, as opposed to on the phone itself. Sometimes this is enforced via technology in the phone, although often it is simply the honor system and not strictly enforced.