The SharePoint 2013 Public Site Tools App is a great app that will only grow over time. Currently it is most useful for creating built-in lists not currently available via the UI for use in the O365 Public Websites.
A lot of organisations would like to do more with the Public Website but find in restrictive - for example wouldn’t it be great to show upcoming events on a calendar on one of your public pages? Unfortunately the Calendar list isn’t available out-of-the-box, but by using this app you can easily create one to use in your Public Website.
You can also create Announcement lists, Task lists, and many others that are unavailable through the current UI.
You can then add these lists into your pages – also as they are SharePoint lists you get all the functionality of creating your own views of the data including sorting and filtering.
For a current view of what lists are present in SharePoint 2013 go here:
PLEASE NOTE: not all lists types will work on a Public Website as some require additional features.