Blockchain – What is Bitcoin Pool API?

Is this an API that connects to a specific mining pool and provides real-time data?

yes.

How do I set it up and where is my data sent?

A breakdown of current mining pools by hash rate is shown here at mempool.space. You should visit each mining pool’s site to see if it offers an API, what data it provides, and how it can be used. For example the Braiins API documentation is here. An API allows your computer to request data from someone else’s server, and if successful, the server returns this data.