These territories are sometimes referred to as the Països Catalans (Catalan Countries), a denomination based on cultural affinity and common heritage, that has also had a subsequent political interpretation but no official status. Various interpretations of the term may include some or all of these regions.
What is the interpretation of the term?
Various interpretations

Diarrheal disease may have a negative impact on both physical fitness and mental development. "Early childhood malnutrition resulting from any cause reduces physical fitness and work productivity in adults," and diarrhea is a primary cause of childhood malnutrition. Further, evidence suggests that diarrheal disease has significant impacts on mental development and health; it has been shown that, even when controlling for helminth infection and early breastfeeding, children who had experienced severe diarrhea had significantly lower scores on a series of tests of intelligence.
What can early childhood malnutrition cause?
reduces physical fitness and work productivity in adults

The origins of the HDI are found in the annual Development Reports of the United Nations Development Programme (UNDP). These were devised and launched by Pakistani economist Mahbub ul Haq in 1990 and had the explicit purpose "to shift the focus of development economics from national income accounting to people-centered policies". To produce the Human Development Reports, Mahbub ul Haq formed a group of development economists including Paul Streeten, Frances Stewart, Gustav Ranis, Keith Griffin, Sudhir Anand, and Meghnad Desai. Working alongside Nobel laureate Amartya Sen, they worked on capabilities and functions that provided the underlying conceptual framework. Haq was sure that a simple composite measure of human development was needed in order to convince the public, academics, and politicians that they can and should evaluate development not only by economic advances but also improvements in human well-being. Sen initially opposed this idea, but he soon went on to help Haq develop the Index. Sen was worried that it was going to be difficult to capture the full complexity of human capabilities in a single index, but Haq persuaded him that only a single number would shift the immediate attention of politicians from economic to human well-being.
Mahbub ul Haq was hoping to shift the focus of development economics to what type of policies?
people-centered policies