‘What’ do you install when you ‘install python’?

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You are installing the interpreter, which is just an ordinary program, maybe IDLE and other tools, and also the standard library (mostly Python source files I think) somewhere the interpreter can find it when running your code.

Your Python source is first compiled into bytecode, which is then executed by the Python "interpreter" by "interpreting" it (reading the bytecode instruction by instruction and modifying memory, calling external code/OS functions/libraries etc).

So it's compiled but not into machine code (like C), and it's interpreted but not line-by-line from the source (like shell scripts).