This is a perceptual classification, based on whether the sounds are perceived as having a secondary, lesser intensity emphasis (grave), or a primary, higher intensity emphasis (acute).
The accents can also be classified acoustically, with acute sounds occupying a higher frequency on the audio spectrum than grave, or in terms of their differing articulations.
Acute sounds generally have high perceptual intensity, and in the case of consonants have been defined as those with an active articulation involving the tongue and a passive articulation involving anywhere on the roof of the mouth that a coronal articulation can reach, that is, from the dental to the palatal region.
The distinction dates from relatively early in the days of acoustic phonetics, at a time that some phonologists believed that one could categorize all speech sounds by a finite set of acoustically-defined distinctive features, which were supposed to correspond to auditory impressions of sounds.
The pioneering publication was Jakobson, Fant and Halle (1951) Preliminaries to Speech Analysis (MIT).