The Public API is a PHP API. Currently it exposes a Repository which allows you to create, read, update, manage and delete all objects available in eZ Publish, first and foremost content, but also related objects like sections, locations, content types, content types groups, languages and so on.
If you used eZ Publish 3.x or 4.x in the past, please check out the Intro for eZ Publish 4.x/3.x developers, it will give you an introduction to the domain language used in eZ Publish 5.x.
For more information on High level architecture overview and cookbook for Public API use, this will be available soon. If you would like to dive into the interfaces and structures available in the Public API, there is a SDK doc here.