香火 (xiānghuǒ) is a cornerstone of traditional Chinese culture, deeply rooted in Confucianism and ancestor worship (祭祖 - jìzǔ). The core belief is that the living have a profound responsibility to the dead. Descendants must provide for their ancestors' spirits in the afterlife by making offerings of food, burning joss paper, and, most symbolically, lighting incense.
A family without descendants to continue these rituals is seen as a great tragedy. The ancestral spirits would be “hungry” and neglected, and the family's entire history would come to an end. This is why the idiom 传宗接代 (chuán zōng jiē dài), “to carry on the ancestral line,” is such a powerful cultural imperative.
Comparison to Western Culture: In the West, people talk about “carrying on the family name” or leaving a “legacy.” This is primarily about social status, inheritance, or personal achievement. 香火 is fundamentally different because it is a spiritual duty. It's not just about the name, but about the active, ritualistic care for the souls of all who came before you. The pressure is not just social, but spiritual and cosmic.
This concept also explains the historical preference for sons (重男轻女 - zhòng nán qīng nǚ), as daughters would traditionally marry into another family and become responsible for her husband's ancestors' 香火. The son was the one who stayed and ensured his own family's flame did not die out.