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Thanks for reaching out!
This is a very good question. As you mentioned the Quark inside Edison is a microcontroller (MCU) unlike the Quark inside a Galileo which is a microprocessor (CPU). If you'd like to learn more about what an MCU and a CPU are, I'd suggest you to read the following documents:
In Edison the CPU is the Atom, it takes care of running the OS and managing the board's peripherals and all the processes running under the hood. The MCU is by default unused, it can be accessed using its SDK (of which you can learn more of in https://software.intel.com/en-us/creating-applications-with-mcu-sdk-for-intel-edison-board).
A CPU does not work on real time as it has to handle so many things at the same time, it instead determines which processes have priority and executes them accordingly. To the human eye this changes and processes happen immediately but electronically it doesn't, the fact that the CPU runs an OS creates a delay which make that actions run far from real time. This is where the MCU comes in handy, the MCU does not have to worry about the OS, the processes and all the other stuff running on your system. You program the MCU and it runs only what you've programmed, this achieves a much more efficient processing time that can almost reach real time.
The occasions where time is key is where an MCU shines the most and it is the same reason why Edison has both an MCU and a CPU.
I hope this information is of help.