Physics of flying discs
A flying disc (aka "Frisbee") is an axisymmetric wing which is gyroscopically stabilized in flight by spinning about its axis of symmetry. As with any object, as a disc is thrown the ambient air is induced to flow around it, generating a combination of aerodynamical forces that lift and slow the disc, as well as aerodynamical torques that cause it to gyroscopically precess (turn). The forces and torques acting on a disk moving through the air depend on its shape, attitude, as well as other factors which may include air speed and spin rate. A disc's intrinsic resistance to aerodynamical forces depends on its mass, and its intrinsic resistance to aerodynamical torques depends on its moment of inertia. A disc is typically operated by throwing it at an angle (it is held in this angle because it acts like a gyroscope), and using the attack angle to generate lift the same way an airplane wing does.
Spin of the disc
The spin of the disc helps to keep the disc stable in flight and prevent tilting. This is because angular momentum stabilizes the disc in the same way that it keeps a gyroscope steady, such that a torque causes the disc to tilt in a direction orthogonal to the imposed torque.