I contacted a website and asked them where they get their data for crypto like Bitcoin, as I am trying to find the place for the most up to date and reliable data on Bitcoin and other crypto. They had sent me an email back saying they get their data from block explorers and pool apis. Block explorers were pretty self explanatory and easy to find and pull data from. But I wasn’t 100% confident in my idea of what a Pool API was. Is it an API that is connected to a specific mining pool that gives you real time data? How do I set it up and where does the data get sent to? Or am I completely misunderstanding what it is?

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Depends on data you are looking for.
Every online block explorer runs a full node in background and shows info from it. You could run your own node (if you have enough space ~700gb at the moment) and query data from it, but unless you are also mining, you will not find any more use of pools api than explorer api.

But this does not include BTC price and market data. Those are gathered from exchange apis.

To run full bitcoin node and query transactions from it (as explorers do) bitcoin.org/en/full-node

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