Fish and visitors stink in three days.
Franklin uses comic exaggeration to suggest that even welcome visitors can become burdensome if they stay too long. Fresh fish quickly becomes unpleasant when kept for several days, and the comparison implies that hospitality can also lose its pleasure when a guest outstays their welcome.
The saying is less a fixed rule about three days than a reminder about social judgement and consideration. Visitors depend on the time, space and resources of their hosts, so a good guest should remain attentive to whether their presence is still convenient. The proverb also recognises that familiarity and prolonged dependence can create irritation even between people who generally like one another. Its broader lesson is that hospitality works best when accompanied by restraint: hosts should be generous, but guests should respect limits and know when their visit has lasted long enough.