a credit agency's best estimate of a person's creditworthiness - i.e. their ability to manage money and credit. A private investigator will be able to interpret this further, and look for evidence of large shifts in credit score, unusual credit checks on their record, and even past bankruptcy. This information is also subject to the FCRA for certain purposes like employment, and generally requires permission from the person being checked.
Businesses, property, and other assets: A private investigator will also be able to compile a list of assets owned by someone. This list can include past and presently owned properties, cars, business, corporations, and other assets they have an interest in. A good background check should also include details on these assets like estimated value, property tax assessments, registration information, photos, dates owned, and more. Quick note - while it is common for people to ask an investigator to find someone's bank statements, this generally cannot be obtained without a subpoena - although sometimes it's possible for an investigator to confirm that an account exists.