Plain English Meaning
The aircraft is built the way the FAA approved and is in good enough shape to fly safely. If either of those is not true, it is not airworthy.
Full Definition
An aircraft is airworthy when it conforms to its FAA-approved type design and is in a condition for safe operation. Both conditions must be met: the aircraft matches the configuration the FAA certified (no unapproved modifications or missing required equipment), and all parts and systems are working properly with required inspections current.
Context Anchor
You will see this term in preflight decisions, maintenance records, aircraft inspections, and FAA discussions of who is responsible for deciding whether an aircraft may be flown.