What does it mean at the green card interview when the officer tells me they need to do "administrative processing?"

Generally, this happens on a case-by-case basis and the U.S. Department of State does not always share what the reason is for administrative processing. If they gave the applicant a list of documents or information to provide, administrative processing is resolved within a few days or weeks of submission of the requested documents. 

For more information about administrative processing, head over here.