The low HDI region in Northern India has comparative advantage within India in agriculture with Fertile Crescent crops and Indian rice. And, so there is been less pressure for this region to depart from a traditional rural agricultural economic model and culture, than there has been elsewhere in India, which goes to why this region is called "the Cow belt" of India (reflecting a rural, religiously conservative predominantly Hindu region), which in a comparative socio-economic sense is somewhat analogous to the "Deep South" in the United States that had a predominantly agricultural economy long after the Northern states in the United States had more fully industrialized.
Conversely, the more developed parts of India aren't optimal for agriculture, which in the South is due to its monsoon climate to which the most valuable staple crops are ill-suited. So, these regions have had comparative advantage for non-agricultural pursuits and have developed accordingly.
An urban commercial economic model is better for pretty much any measure of development from per capita GDP, to Human Development Index, to life expectancy, to average number of of children per woman per lifetime (more precisely Total Fertility Rate), to pretty much any other measure you use. While each of these indexes measures something slightly different, in the case of India, the disparities are so extreme that these distinctions become irrelevant and any of them will do.
In India, as in China, as in Europe, as in Africa, as in Latin America, and as in the United States, per capita productivity is greater in places with higher population density (adjusting only for current, easily exploitable natural resource deposits like oil and natural gas). The linked 2011 economic study using U.S. notes, consistent with the larger literature in economics, that: "we find that a doubling of density increases productivity by 2 to 4 percent." And, over time, this edge in productivity produces compounding returns.
The image below is a district level population density map of India:
Higher population density and the productivity gains that come with it, emerge much more naturally when you have an urbanized commercial economy because your region is comparatively ill suited to being a "breadbasket", than when your region's business model is based upon agriculture.
The effect is somewhat similar to the "coal curse" observed in global economic development, which shows that areas that were "blessed" which rich coal resources focused on mining those resources and failed to develop as strong of a broader based commercial economy. As a result, places with historically rich coal resources tend to lag economically behind places that had few fossil fuel resources.