The term 国计民生 is deeply rooted in a political philosophy where the state holds a primary and paternalistic responsibility for the welfare of its people. In Chinese culture, a government's legitimacy is intrinsically linked to its ability to successfully manage the 国计民生. If the people are prosperous and their lives are stable (a state described as 安居乐业 - ānjūlèyè), the government is seen as effective and holding the “Mandate of Heaven,” a classical concept that has evolved into modern political legitimacy.
This is a formal and “heavy” term. You will almost never hear it in casual, everyday conversation. Its use is reserved for serious and official contexts.