The Law of Compound Motion tells us that we should think of moving object's path as being made up of two separate parts of components. For examples, if you throw out a basketball at 60 degree and air resistance is ignored, then this is a projectile motion and the basketball can be thought of moving vertically and horizontally at the same time. The basketball is moving horizontally at constant velocity while the basketball is moving vertically with an acceleration of 9.8 m/s2. The motion in vertical direction does not affect the motion in horizontal direction.
To help you better understand the Law of Compound Motion, look at the picture below:
As you can see, the velocity at both two points can be decomposed as vertical velocity and horizontal velocity. That is the Law of Compound Motion