Android devices usually have one or more sensors used to detect the orientation of the phone, such as whether it is lying down flat or tilted at some angle. These sensors can be very sensitive and may sometimes require re-training to know which direction is up. This G-Sensor calibration allows you to do this re-training.
You will be asked to place the phone on a level surface such as a table and to press a button.
You should not need to do this often - it is recommended you do this only once when you are setting up the phone, and from then on it can be re-visited only if you have specific problems with the sensor.