In short, as it flies through the air, one wing travels faster than the other. The unbalanced force that results from this difference is what causes the boomerang to turn and, if it is thrown just right (wind direction and speed must be accounted for), it will come back to the thrower.
What causes a boomerang to return?
When the boomerang is thrown with high spin, a boomerang flies in a curved rather than a straight line. When thrown correctly, a boomerang returns to its starting point. As the wing rotates and the boomerang moves through the air, the airflow over the wings creates lift on both "wings".
Why is my boomerang not coming back?
Troubleshooting. Reassess your throw if your boomerang won't come back. If your boomerang is failing to return to you, the reason is one of two things: your boomerang is of poor quality, or your throw is incorrect.