The Local Action Center allows you to select disparate edges or polygons in your model and act on them as one, locally. This means that you move, rotate or scale each selected edge or polygon at its local origin rather than a single origin for all the disparate elements. The Local Action Center works on multiple layers at a time.
Using the Move tool with a Local action center will end up with the same result as prior to their addition, but Rotation is a different story. The animation shows the Rotate tool (Y) being used on polygons on different layers, using different Action Centers:
The Transform tools are also greatly improved with this addition to the Action Centers. We show Stretch (H) with the different Action Centers, but Scale (Shift-H) is similar:
Local also works with Symmetry: