Gyroscopes in consumer electronics sense angular velocity (angular rate) along one rotational axis. These does not give you the absolute orientation as they are (they give you velocity, or rate, not the actual degree). In order to obtain the orientation from these sensors, you need to "integrate" the rate values from a known initial orientation. Gyroscopes are usually tri-axial as well, making 6-degrees-of-freedom "inertial measurement unit" with 3-axis accelerometers.
Magnetometers are simply a compass. A linear magnetometer measures direction and strength of magnetic field along one dimension. In the absence of external disturbance, it can be used to detect earth magnetic field, which always points to (magnetic) north. For magnetometers, this "reference" also contains horizontal component ("north"), from which you can read off lateral orientation of the device, unlike accelerometers. However, the earth magnetic field is very weak compared to common disturbances around (steel furniture, car passing by, etc), so not quite an accurate source of yaw orientation.
Each of the common sensor types: accelerometer, gyro, magnetometer and GPS have some overlap, but different characteristics.
An accelerometer can tell you your tilt relative to the earth's surface (2 axes) but not your heading. In theory, if you knew where you were starting, you could add up acceleration to give you an estimate of position, but in practice, errors add up very quickly. But until they drift too far away from reality, you can use them for very high frame rate estimates of position.
A magnetometer can tell you your heading if you hold it parallel to the ground. But combined with the tilt readings from a 3-axis accelerometer, you can get your heading regardless of how you're holding your device.
Gyros are great at giving rotational velocity, but have no absolute reference. Again, if you knew where you were pointing initially, you could get very high frame rate estimates of orientation. But it, too, drifts quickly.
The combination of accels plus gyros gives you an Inertial Navigation System, aka Intertial Measurement unit. But you need very high accuracy instruments for this to stay accurate enough to be useful for very long.
Finally, the ultimate:
Add in a GPS. These give you position, but not orientation. But you only get data once per second, so you couldn't steer a car, plane, or rocket with it. So you fuse the low frequency, absolute, GPS and magnetometer data with the high frame rate gyro and accelerometer using something like a Kalman filter. This is a modern navigation system, and it's pretty damn good.
I'll stop before bringing in differential, kinematic, and phase-based GPS, which make it even better using multiple GPS receivers and other improvements to get even higher accuracy...
The accelerometer, gyro and the magnetometer form the Inertial Measurement Unit (IMU). The information obtained from each of these sensors is combined in order to get the best position information since one is more sensitive to other depending on the scenario it is being put into.
An accelerometer's primary function is to react to and sense linear acceleration. This gives you the position directly. Also, because the gravitational pull is acceleration, this can give you the position of the device perpendicular to the earth's surface. So, the device motion can be tracked using this.
The gyro basically gives you the changes in rotational orientation of the device (from a reference or known orientation of the device).
The magnetometer determines the orientation of the device with respect to the Earth's magnetic fields.
As you can see, the accelerometer will serve the purpose in case of a mobile device (since it can respond to rotational orientation to an extent), it is best to appropriately integrate information from all of them.
A combination of the three, accelerometer, gyroscope and a magnetometer forms an inertial measurement unit.
An accelerometer measures force in each of its axis, if it is a 3 axis accelerometer, then on all the three axis.
A gyro measures the angular velocity with respect to the body axis.
And a magnetometer gives you the orientation with respect to magnetic north and magnetic south of the earth's magnetic fields.
Sensor readings from just an accelerometer is too noisy for any productive use, although it still can be implemented.
And a gyro is prone to drift. Say it is tilted in the yaw axis and stopped after say 't' secs, the gyro will still continue to show some variation even after it is stopped.
But a combination of all the three by by means of kalman filtering or complementary filtering, can give out noiseless and very usable signals.
Accelerometer: Any kind of linear acceleration, including the orientation of the device because of the acceleration due to gravity from Earth. Can determine rotation to some point due to the sensor itself often isn't in the center of rotation, causing acceleration by centripetal forces. Doesn't work when in the center of rotation, cannot distinguish rotation from acceleration.
Gyroscope: any rotation, unaffected by acceleration.
Magnetometer: orientation and direction by determining the direction of Earth's magnetic field. Can be interfered by the environment, doesn't work everywhere on Earth, potentially useless in a couple of decades due to pole switching.
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