These characters combine to literally mean “to leave a stink for ten thousand years.” This vivid, almost physical metaphor emphasizes the enduring and disgusting nature of the person's legacy. It's not just a bad memory; it's a permanent, foul odor in the annals of history.
In Chinese culture, history is often seen as the ultimate judge of a person's character and life's work. The concept of one's name or reputation (名声, míngshēng) after death is of paramount importance. The ultimate goal for a virtuous person is to 流芳百世 (liú fāng bǎi shì) - “to leave a fragrant reputation for a hundred generations.” 遗臭万年 is the absolute, terrifying opposite. It is the ultimate curse, a condemnation not just by one's contemporaries, but by all future generations. A useful comparison to a Western concept is “to go down in infamy,” like Benedict Arnold in American history. However, 遗臭万年 carries an even heavier weight of moral and historical judgment. While a figure like the outlaw Jesse James might be “infamous” but also romanticized, there is zero romanticism in 遗臭万年. It is reserved for figures of pure villainy, particularly traitors and tyrants. The classic example is the Song Dynasty official Qin Hui (秦桧), who betrayed the celebrated general Yue Fei (岳飞). To this day, statues of Qin Hui and his wife are often depicted kneeling in shame, and visitors sometimes spit on them, showing how the “stench” of his name has indeed lasted for centuries.
遗臭万年 is a very strong, formal, and literary idiom. It is not used in casual conversation for minor wrongdoings. Its use is reserved for situations of extreme moral condemnation.
The connotation is always 100% negative and carries a sense of profound disgust and final judgment.