Compass

First of all there are three sensors that are useful for determining position and orientation in smartphones, but they measure different things.

Magnetometer A magnetometer measures magnetic fields. Because the earth has a significant magnetic field, the magnetometer can be used as a compass. As such it is useful to determine absolute orientation in the NEWS plane.
Accelerometer. An accelerometer measures accelerations. This is useful to measure changes in velocity (directly, as the acceleration is the first time derivative of the velocity) and changes in position (by integrating the signal). They are usually used for measuring small movements. Also note that gravity acts like a continuous acceleration upward (via Einstein's equivalency principle), so a multiple-axis accelerometer can also be used as an absolute orientation sensor in the UP-DOWN plane.
A gyroscope measures either changes in orientation (regular gyro or integrating rate gyro) or changes in rotational velocity (rate gyro).
e-Compass/ Digital compass

The e-Compass is an important sensor for smartphones and tablets as it maintains alignment of the display with the user's orientation.

e- compass is usually based on a magnetometer sensor which provides mobile phones with a simple orientation in relation to the Earth's magnetic field. As a result, your phone always knows which way is North so it can auto rotate your digital maps depending on your physical orientation.