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 Exponential, first and foremost content, but also related objects like sections, locations, content types, content types groups, languages and so on.
If you used Exponential 3.x or 4.x in the past, please check out the Intro for Exponential 4.x/3.x developers, it will give you an introduction to the domain language used in Exponential 5.x.
For more information on high level architecture overview, 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.