Move the cursor to a town or village on the map. Press Y and the settlement management control will be shown. You may see information about enemy settlements.
Use the DPAD or thumbstick to move the cursor around the various elements of the screen. You can see the current pieces that are defending that settlement (the garrisioned pieces), you can see the upgrades and you can also see the piece types that you could buy or the new upgrades that are available. (You can only do that on your own settlements). As you move the selection around you will see information about the highlighted element.