What does the A.A.B. Designation stand for?

Answer 1

As you asked in the insurance category perhaps you meant AAI?

Accredited Adviser in Insurance (AAI) is the result of a joint effort of the Insurance Institute of America (IIA) and the Independent Insurance Agents and Brokers of America (IIABA).

Candidates must pass an examination for three of the following courses to earn the designation:

* AAI 81: Foundations of Insurance Production
* AAI 82: Multiple-Lines Insurance Production
* AAI 83: Agency Operations and Sales Management

Answer 2

Depends on the context. but it's probably an associate degree in business (Associates of Arts and Business)