Unfortunately, the terms airworthy and unairworthy are not specifically defined in the regulations. The terms have achieved some definition through FAA enforcement cases and in FAA legal interpretations. The precedent set in these ways suggests that, to be airworthy, an aircraft must satisfy two conditions. First, the aircraft must conform to its type certificate, as modified by supplemental type certificates and airworthiness directives, if any. Second, the aircraft must be in a condition for safe operation. This, of course, is the legal definition; a practical, simple definition is much harder to come by.
Certainly, the determination about whether or not an aircraft is airworthy begins well before takeoff. But what do the regulations require of the pilot who departed in an airworthy aircraft and is in midflight when something occurs that affects the operation of the aircraft? Broken down, the regulation first requires that the pilot assess whether the aircraft has been rendered unairworthy. Second, the pilot must abide by the regulation's requirement to discontinue the flight.
If you are en route and a mechanical, electrical, or structural condition has occurred, there's a good bet that the aircraft has, at least, fallen out of conformity with its type certificate. In addition, the aircraft probably cannot be operated safely. The circumstances we are talking about in this context do not include engine failure - then you no longer have the option of continuing the flight. Rather, we are talking about the type of circumstance where, for example, the oil pressure gauge is fluctuating, suggesting an oil leak; or the rpm has dropped and applying carburetor heat does not cure the problem; or you experience a bird strike that leaves a dent in the leading edge of the wing.
Having made the determination that the aircraft may be in an unairworthy condition, how may the pilot satisfy the requirement of the regulation to discontinue the flight? Certainly, in common parlance, this means that the pilot should land. But where and when? Should the pilot land at the next available strip of land; at the next available airport; at the next available airport with long runways, emergency equipment, and maintenance facilities; or may the pilot legally continue flying to his or her home airport?
Again, FAA enforcement cases and agency interpretations seem to be the only places from which we may glean some guidance. Basically, the FAA has interpreted and enforced the regulation as requiring that the flight be discontinued at the first available location that is consistent with the safe operation of the aircraft, considering such factors as the capabilities of the aircraft, runway length, and runway composition. That is, you may continue to fly to a suitable landing point that will allow the aircraft to be safely landed, even if it means passing up other questionable landing sites. But, you may not pass up a suitable landing site in favor of waiting to land at a preferable airport. Safety is paramount; convenience and comfort are not.
The FAA's regulation is not clear in its guidance, and the case law interpreting the regulation is somewhat inconsistent in its application. At best, it seems that the regulation requires the pilot to exercise prudent judgment, in the conservative interest of safety. This may ultimately be second-guessed. Still, doing your best to understand what may render your aircraft airworthy, or unairworthy, and where you must land an aircraft that has been rendered unairworthy in flight should help you to avoid an accusation of noncompliance by the FAA.