Tethering (also known as phone-as-modem and hotspot) is a feature in Android and iOS devices where the internet connection from the device can be shared with other devices. There are three ways to share an internet connection in mobile tethering: Wi-Fi, Bluetooth, and USB.
Tethering in smartphones may be unavailable if the phone is distributed by a wireless carrier. This can be made available by one-time payment to the carrier to enable tethering, or by rooting or jailbreaking Android or iOS respectively.
Connecting to the sharing device is like connecting to a router, which is why some applications and games use tethering to create a local network, eliminating the hassle to have a router as the access point.
The rate of the battery draining depends on the method of tethering. In USB, it is practically zero since it also charge as Ethernet packets pass to and from the phone. In the case of Wi-Fi and Bluetooth, the latter drains slower than the former at the cost of speed.