What is the significance of "microcontroller based on microprocessor"?
ARM is the CPU core, which can be used to implement a microprocessor or a microcontroller.

The full sentence you referenced is:

The STM32 family of 32‑bit Flash microcontrollers based on the ARM® Cortex®‑M processor is designed to offer new degrees of freedom to MCU users.

Clearly this is largely content-free marketing babble.  Don't pay much attention to it.  It actually never says "microprocessor".  It refers to the ARM core as a "processor", which isn't strictly right either.  It's just a core, which can be used to implement various kinds of processors.

The core is more like the engine of a car.  You license the design from ARM, but can heavily configure it to your needs, and putting the chassis and wheels around it is your job.  You can make the result a sports car, a pickup truck, or various other types of vehicles.  The marketing babble above is like saying "We've based this pickup truck on a sports car".  No, they haven't.  They've base the pickup truck on the same basic engine technology others have used to make a sports car with.

Again though, the important point is that this is all marketing babble.  There is nothing useful to see here.  Move along everyone.