Fortunately, the technical details of buying APLI are not your concern.
Before exploring those fundamentals, here are two matters to help you put APLI in context.
An APLI policy is designed to protect past, present, and future directors, officers, committee members, trustees, employees, volunteers, and the nonprofit entity itself against allegations of wrongful acts committed in the management of the organization.
If your answer is no (and some APLI policies are not duty-to-defend policies), be aware that you (that is, any person or entity defined as "insured") may have to hire an attorney to provide defense, pay the bills up front, and then apply to the insurance company for reimbursement at a later date.
The key to understanding the APLI policy is that it covers only money damage losses, not claims for bodily injury or property damage.
Premiums for APLI coverage are not insubstantial (minimum premiums start in the $1,750-$2,000 range and rise based on revenue).