In the .zip file you downloaded, you will see the 'Move Anchor Point.jsx' and the 'map_images' folder. Select and copy both items.
You need to paste them into the 'ScriptUI Panels' folder for your version of After Effects. (You must have After EffectsCS3 or higher to use the Move Anchor Point script.)
Mac: ~/Applications/Adobe After Effects YOUR VERSION/Scripts/ScriptUI Panels
Windows: C:/Program Files/Adobe/Adobe After Effects YOUR VERSION/Support Files/Scripts/ScriptUI Panels
** If you do not have any ScriptUI Panels installed already, you should verify the spelling and placement of the 'ScriptUI Panels' folder. Capitalization and spacing is important. If the folder is not correctly named and in the correct location, the script will not be visible in the 'Window' menu.
Now start up After Effects. You will see 'Move Anchor Point.jsx' at the bottom of the 'Window' menu. Select it to open the Move Anchor Point panel. If After Effects was already open, you must restart the program before it will be visible in the 'Window' menu.
Move anchor point allows you to quickly move the anchor point of a layer to a new location without changing the visible position of the layer. The anchor point can be moved to one of nine preset positions, and new in version 2.0 it can also be moved precisely to a custom position.