what does Drupal API mean? What does it mean when someone says Drupal API? Does that phrase include drupal hooks, theme functions and every other drupal term or is it used as a synonym for api.drupal.org 

I am really confused please define it for me to understand it easily.

Many thanks
It's a generic term to encapsulate all the programming interfaces Drupal provides. Any further meaning would have to be inferred from the context of how it was used (FWIW, I've never heard "Drupal API" to refer to the documentation site api.drupal.org). 

When specifying a particular component of the Drupal API, you'll often see it labeled with its functionality (e.g. Drupal Routing API, Drupal Batch API, etc.) to clarify what part of Drupal's API is being discussed.