Your medical certificate represents an aviation medical examiner's assessment that at the time of your physical exam, you met the requirements to hold a medical certificate, and could reasonably be expected to remain able, for the duration of the certificate.
The medical certificate is valid so long as you are medically fit. If at any time you are not fit, the medical certificate is not valid.
For example, if you develop a head cold and cannot fly, although you hold a medical certificate, it is not valid until you are fit to fly again. You do not need to notify the FAA, but you cannot exercise the privileges of that certificate if you are not fit. If something occurs which makes you unfit, then your certificate is not valid; it is always predicated on you being medically fit. If something occurs in the interim that affects your health in a way that requirements exist to remain fit, you must report it at the time of your next medical. If, for example, you were to begin having vision problems, and obtained a prescription for glasses, you'd need to wear them to meet the standard of your medical certificate, even though you haven't been back yet to the AME, and don't have that limitation displayed on your medical certificate.
Some things may occur which changes your medical status. A heart attack. Certain cancers. Kidney stones. The FAA may require, for example, evidence and medical documentation that you are free of kidney stones and statements with evidence showing that the incidence was a one-time occurrence, and will not happen again, or is not likely to happen again. Following a heart attack, the medical certificate is invalid for use and further documentation and testing is required before one can return to a legal, medically fit status. The heart attack marks a point during which the medical certificate has been invalidated by a health condition, and until the requirements are met once again to be considered medically fit, one is not legal to use that certificate to exercise airman privileges.
Other conditions, like a headcold, a root canal, or other relatively superficial events may temporarily prevent exercising airman privileges, but do not need to be reported until the date of the next medical application
When in doubt, it's a wise idea to contact your AME to discuss any reporting requirements.