How do phones sense your orientation?

All modern smartphones have a gyroscopic sensor. A gyroscopic sensor is a sensor that detects the angle the phone is at. This is used for your phone to auto-orient, VR, etc. It is also used in airborne vehicles especially attack crafts that go at dangerous angles. 

Have you ever played with a gyroscope? Toy gyroscopes are amazing toys which are not really expensive but can teach you an awful lot of science. Sorry, they can help you learn an awful lot of science. A gyroscope always maintains its angle despite the angle of the object it is suspending from. One way often used to depict this is that you take a bicycle tyre and after tightly inserting an approx 12" long stick through the ball bearing, tie any study cord to the other side of the stick. Then hold the stick at 90 degrees to the cord and spin the wheel. You are going to notice that even when you leave the stick, the stick is going to maintain its perpendicular angle to the chord. As the speed of the tire starts to slow down the angle increases until it becomes a 180-degree angle from the chord. 

A smaller way of replicating the above experiment at home is: take a fidget spinner (I will do an article about this later sometime) and take off the caps. After that, take a stick (you can use a pencil also) that fits perfectly in the inner ring of the ball bearings. Try and use a stick/pencil that fits perfectly (you can wrap some tape around the pencil if it's not wide enough). After that, tie a string to the other side of the stick/pencil and hold the stick perpendicularly to the rope. Hold the string or tie it somewhere, from where it suspends freely. Spin the fidget spinner. The results will be similar to as seen above with the cycle tyre.

Your phone has something like this that detects angles, though a much more miniaturized version that fits into the device. If the phone is tilted, the gyroscope will complete a circuit.