Local offset controls whether the initial position of the object of the pattern is ignored. The position of the object is completely determined by its position in the pattern. If Local offset is checked, then the feature's position influences the created pattern.
Using an object's position in a pattern can be tricky. For example, use local offsets to create a pattern of profiled features, say, a radial pattern of profile pockets. The recommended procedure is:
Create the profile relative to the UCS.
Enter the center of the pattern as XYZ coordinates.
Enter 0.0 as the radius.
The pockets share the relative position to their center as the initial curve did to its UCS.