What defines the position of White Dwarf stars on the H-R diagram?
Extremely low luminosity despite very high surface temperature.
White Dwarf stars occupy the lower-left region of the H-R diagram. These stellar remnants represent the end stage for low- to intermediate-mass stars after they have shed their outer layers. Although they are incredibly hot, sometimes hotter than certain Main Sequence stars, their defining characteristic in this region is their extremely low luminosity. This dimness is a direct consequence of their size, as they have collapsed to become physically very small, often comparable only to the size of the Earth. Their location contrasts sharply with the Giants; both are hot, but White Dwarfs are dim due to size, whereas Giants are bright due to massive expansion.

#Videos
HR Diagram Explained - Star Color, Temperature and Luminosity