Plain English Meaning
A step-by-step training plan that the FAA has officially signed off on. The school must teach according to it, and they can't change it on their own.
Full Definition
A training syllabus that has been formally reviewed and accepted by the FAA for use in a specific certificated pilot training program, such as one operated under 14 CFR Part 141 or Part 142. Once approved, the syllabus must be followed as written, and any substantive changes require FAA re-approval.
Context Anchor
Seen in instructor training, flight school course planning, and discussions of structured training programs.
Derivation
"Approved" comes from the Latin approbare, meaning to assent to or sanction. In this context it carries its specific FAA meaning: formally accepted by the agency, not merely allowed.