STM32F429 / STM32F439 read-while-write from two memory banks. Prevents stalling CPU?
Flash are non-volatile memory device, so you may want to save some system configurations or calibration data in it. And STM32 gives you opportunity to protected them from read/write, so this may save you from another EEPROM, or other external non-valatile memory devices. 
According to section 3.6.5



  This feature allows to perform a read operation from one bank while an
  erase or program operation is performed to the other bank.


When you are executing/reading code/data from bank1, you can executing erasing/programming operations on bank2. For example, your code is running in bank1, and you execute some codes to start one "earas" operation on bank2, once the "erasing" start, you needn't wait the operation done, you can continue to do other things (but can't execute codes to do erasing/programing on bank2). Then, after some while, you check the BSY bit to see if the erasing done. So your code executing and erasing are doing at the same time, no waiting needed.

According to "Read from bank 1 while erasing bank 2":


  While executing a program code from bank 1, it is possible to perform
  an erase operation on bank 2 (and vice versa). Follow the procedure
  below: 
  
  
  Check that no Flash memory operation is ongoing by checking the BSY bit in the FLASH_SR register (BSY is active when erase/program operation is on going to bank 1 or bank 2)...
  


So, there is no "priority", you can't fire two "erasing/programming" operations at the same time. The first fired always be served first. And you must wait until one erasing/programming operation done, then fire a new one.