A boomerang travels in more or less a circular path. The motion is a combination of various physical principles, for example, aerodynamic lift and circular motion. You have to get these physical principles just right when throwing a boomerang. Think of the two arms of a boomerang as being like the wings of an airplane. The faster they move through the air, the more lift they generate. A boomerang spins as it moves through the air and the combination of spin and forward speed means that some parts of the boomerang are moving faster than others. This means that the boomerang traveling sideways so the net lift is towards the center of the circle that you see the boomerang move on.
Another important physical principle is the non-uniform lift. The non-uniform lift generates torque. This causes the gyroscopic effect to come into play. A spinning boomerang is really no different to a spinning gyroscope and the gyroscopic effect makes the boomerang turn around at just the right rate.
Another aspect is gravity. You need a bit of lift force directed upwards. Otherwise, the boomerang will just drop to the ground. This explains why you need to throw the boomerang at an angle giving it a tilt. It also explains why a good boomerang will increase its tilt angle as it slows down. This is called lying over. A boomerang that has slowed down and laid over is easy to catch
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