Arduino due slow clock
The slow clockr is primarily used for the real time clock (RTC) module inside the SAM3X chip.  It can also be routed to other places when you want a low speed clock source, but the only places it is actually required are the RTC and the watchdog. 

The slow clock can be generated from an internal RC oscillator instead of requiring an external crystal, but the accuracy and stability of the RC oscillator is many orders of magnitude worse than a crystal.  Trying to use that for the RTC module will result in the clock drifting over time.  The watchdog won't really care if the clock isn't perfectly accurate.