What is the westerly index?
The only mention of it I could find in relation to a CPL is from a New Zealander CPL syllabus (govt.nz; PDF).
Including NZ in the search leads to this definition:

The westerly index is the Trenberth Z1 index (Trenberth 1976), which is the departure of the monthly mean pressure difference between Auckland and Christchurch (near 44°S) from its mean over the 1961–90 period.
— journals.ametsoc.org

From that definition, a pilot needs to be aware of the pressure difference between Auckland and Christchurch.

Others here may be able to expand on its usage (feel free to reuse, anyone).
From an Earth Science perspective, I asked on the sister site: What does a change in the mean pressure across 750 km indicate/signify?