From the genus name Hedwigia, and the Greek diminutive suffix -idium.

From Hedwigidium integrifolium: 

Plants brown below, olive-green to pale yellow-green above. Stems intertwined and richly branched; stoloniferous stems present. Stem leaves erect to erecto-patent when dry, erect-spreading or spreading when moist, ovate-oblong to ovate-lanceolate, concave, 1.25–2.46 mm long, 0.57–1.04 mm wide; apex acute to acuminate, pigmented, rarely hyaline at the very tip; margin recurved, entire. Central basal laminal cells elongate, thick-walled, porose, ±papillose; cells 10–20 × 4–10 µm, becoming short-rectangular to isodiametric towards the apex, with thick slightly sinuous walls and numerous small simple papillae per cell, usually over the cell walls. Leaves of stoloniferous stems ovate, gradually tapering to an acuminate filiform apex, concave, plicate near the margin.

Perichaetia terminal; perichaetial leaves oblong, similar to stem leaves but much more elongate, with a very large section of smooth elongate laminal cells in the lower part of the leaf, not ciliate. Seta c. 1 mm long. Capsule ovoid, widest below the mouth, slightly grooved when dry, abruptly tapered to the neck; operculum rostrate. Spores 22–28 µm long, striolate.

Distinguished from Hedwigia by the short seta, weakly plicate leaves, simple rather than branched papillae, and the stoloniferous stems.

A single species occurs in Australia: Hedwigidium integrifolium.

Hedwigidium Bruch & Schimp., in Bruch, Schimper & von Gumbel, Bryol. Europ. 3: 155 (1846). Type: H. imberbe Bruch & Schimp. [= H. integrifolium (P.Beauv.) Dixon]

Gilmore, S.R. (2012). Australian Mosses Online 4. Hedwigiaceae. Australian Biological Resources Study, Canberra. Version 10 April 2012. http://www.anbg.gov.au/abrs/Mosses_online/04_Hedwig.html