Proper Purpose

It may be easier to get at this from the other direction and figure out what is considered an improper purpose. Laws in many states frown on things like fishing expeditions (ie, requesting reams of records in order to nitpick or to search for evidence of wrongdoing when the owner has no valid reason to suspect wrongdoing). Other times owners may ask to see records that they're not entitled to see (eg. things that must be kept confidential).

Things like this often boil down to the difference between wanting to find out information for your own benefit (such as understanding your community's financials) vs. wanting to stir up trouble. Proper purpose is usually specific and targeted, improper purpose is generally vague and wide ranging.

The links below may be helpful.

https://www.vahoalaw.com/board-member-responsibilities/requests-for-association-records-what-are-the-rules-of-the-road-2 (The article references Virginia laws pertaining to condos and to HOAs).

Text of the relevant laws:
https://law.lis.virginia.gov/vacodepopularnames/virginia-condominium-act/
https://law.lis.virginia.gov/vacodepopularnames/property-owners-association-act/