Akonadi aims to be an extensible cross-desktop storage service for PIM data and meta data providing concurrent read, write, and query access. It provides unique desktop-wide object identification and retrieval.
Akonadi framework provides two parts: the server, and client libraries to access the data managed by the server.
If you are an application developer and want to access and interact with data stored in Akonadi, you should read the Akonadi client libraries documentation.
If you are interested in working on the Akonadi framework itself, you can read more about the internals of the Akonadi Server and the protocol in the Akonadi server documentation.
You can also read a bit more about history of Akonadi