The expiry date is the manufacturer's guarantee that the medicine keeps its full strength and quality up to that point when stored correctly. After expiry, many medicines slowly lose potency, which means they may not work as well, a real problem for medicines you depend on.
For most solid tablets, taking one shortly past its date is unlikely to cause harm, but reduced effectiveness can be dangerous when the medicine is treating something serious. For critical medicines such as those for heart conditions, severe allergies, infections, insulin or emergency use, an expired product should never be relied upon. Liquids, eye drops and anything requiring refrigeration degrade faster and should be discarded promptly after expiry.
The safest approach is to replace expired medicines and dispose of them properly, ideally by returning them to a pharmacy. If you are unsure whether an expired medicine is still usable, ask your pharmacist.