Abbreviation: HRI = "High Refractive Index" (Nikon)

The abbreviations means "High Refractive Index"

Explanation from Nikon

With a refractive index of more than 2.0, one HRI lens can offer effects equivalent to those obtained with several normal glass elements and can compensate for both field curvature and spherical aberrations. Therefore, HRI lenses achieve great optical performance in an even more compact body.