The difference in pressure causes the Frisbee to rise or lift. This is the same principle that allows planes to take off, fly and land. Another significant factor in the Frisbee's lift is Newton's Third Law which states that for every action there is an equal and opposite reaction. The air is deflected downward by the Frisbee's tilt, or angle of attack. Spinning the Frisbee when it is thrown, or giving it angular momentum, provides it with stability.
Angular momentum is a property of any spinning mass.
Throwing a Frisbee without any spin allows it to tumble to the ground. The momentum of the spin also gives it orientational stability, allowing the Frisbee to receive a steady lift from the air as it passes through it. The faster the Frisbee spins, the greater its stability. Resources Horowitz, Judy and Bloom, Billy. Frisbee, More Than Just A Game of Catch.