In short
Off-label prescribing is the practice of a licensed prescriber prescribing an approved drug for an indication, patient population, dose, or route of administration that has not been specifically evaluated and approved by the relevant regulatory agency for that use.
Drug approval by agencies like the FDA is indication-specific: a regulator approves a drug based on trial data for a defined use (a specific disease, population, dose range), but once approved, a physician has legal latitude to prescribe that same drug for a different, unapproved use, based on their clinical judgment — this is a well-established, longstanding, and legal part of medical practice in most jurisdictions, not a loophole or a red flag by itself. Many mainstream, well-accepted treatments in numerous specialties began or continue as off-label uses of previously approved drugs.
In longevity medicine specifically, several of the more prominent compounds discussed on this site are prescribed off-label for anti-aging purposes: rapamycin (approved for transplant immunosuppression) and metformin (approved for type 2 diabetes) are both, in this context, being used for an indication — general longevity or biological-age improvement — that has not itself been evaluated and approved by any regulator, because no drug currently carries an approved "aging" or "longevity" indication anywhere in the world.
The legality of off-label prescribing does not, by itself, indicate the strength of evidence for that specific off-label use — evidence quality has to be assessed individually for each drug and use case, which is why this site's evidence-grading system (see how we grade evidence) evaluates a compound's off-label longevity use on its own merits rather than treating "a doctor can legally prescribe this" as equivalent to "this has been shown to work for this purpose."