What does granularity mean?
If you think of the background task as being (as it may well be) triggered from a timer interrupt, the granularity is basically how long that timer interrupt will last while it's processing the background task.

It's in effect the percentage of run-time given to processing the background task, and how much processing time is taken away from your foreground task.

Each activation of the background task will take X clock cycles.  These clock cycles will be on one solid block.  Your main foreground task will be interrupted for those X clock cycles.

The word "granularity" comes from the background task causing a "graininess" or "lumpiness" in the execution of the foreground task.