Tethering
Sharing the Internet connection on a smartphone with a computer is called tethering. The smartphone must have a data connection and either be physically connected to a computer using a USB cable (or similar cable) or transmit a Wi-Fi or Bluetooth signal for the computer to connect to and receive the Internet connection. Many smartphones have the capability of tethering built-in, while others require special software (app) to perform the tethering.
Cell phone carriers typically charge a monthly fee to allow a person to use their smartphone for tethering. Some people get around this by rooting their phone, but this is technically not legal and it circumvents the carriers' monitoring systems. If a person is caught tethering their phone without paying for the service, the carrier may terminate the person's contract and can invoke fees associated with early termination or breach of contract. It's best to play it safe and pay the monthly fee, which then allows for tethering to any Internet capable device, including computers, without penalty.
Also see: Cell phone definitions, Smartphone