Not the points exactly. (There doesn't seem to be any particular purpose for those other than if you just like seeing your overall Achievement standing as a numeric score.) There are, however, a number of individual Achievements that reward items. Once you earn one of these Achievement items, you can pick it up from an NPC named Jonathas in Old Gridania. Only a few of the Achievements reward such items, though, and they tend to be ones with relatively long-term goals that take quite a while to reach.

On the achievements window, the list of possible achievements in a given category will include a little treasure chest icon by the name of each of the ones that reward an item, and if you select that achievement to show its details it will tell you what the item is.