"partly decomposed vegetable matter abundant in moist regions of northern Europe," where, especially in Ireland, it was an important source of fuel, c. 1200 in Scottish Latin, of unknown origin, probably from a Celtic root *pett- (source also of Cornish peyth, Welsh peth "quantity, part, thing," Old Irish pet, Breton pez "piece"). The earliest sense is not of the turf but of the cut piece of it, and the Celtic root may be from the same PIE source as piece. Peat-bog is by 1775; peat-moss (mid-13c.) originally was "a peat bog;" the meaning "sphagnum moss" (the type that grows in peat bogs) is by 1880.
also pot-hole, "more or less cylindrical cavity from a few inches to several feet deep in rock," 1826, originally a geological feature in glaciers and gravel beds, from Middle English pot "a pit, a hollow, a deep hole for a mine or from peat-digging" (mid-15c.; 12c. in place-names), now generally obsolete in those senses, but preserved in Scotland and northern England dialect; perhaps ultimately from or related (via a Scandinavian source) to pot (n.1) on notion of "deep, cylindrical shape." Applied to a hole in a road from 1909.
the meanings "mass of small, cryptogamous, herbaceous plants growing together" and "bog, peat-bog" are the same word: Old English meos "moss plant" and mos "bog;" both are from Proto-Germanic *musan (source also of Old High German mios, Danish mos, German Moos), also in part from Old Norse mosi "moss, bog," and Medieval Latin mossa "moss," from the same Germanic source.
These are from PIE *meus- "damp," with derivatives referring to swamps and swamp vegetation (source also of Latin muscus "moss," Lithuanian mūsai "mold, mildew," Old Church Slavonic muchu "moss"). The Germanic languages have the word in both senses, which is natural because moss is the characteristic plant of boggy places. It is impossible to say which sense is original. The proverb that a rolling stone gathers no moss is suggested from 14c.:
Selden Moseþ þe Marbelston þat men ofte treden. ["Piers Plowman," 1362]
Moss-agate "agate stone with moss-like dendrite forms (caused by metallic oxides)" is from 1790. Scott (1805) revived 17c. moss-trooper "freebooter infesting Scottish border marshes" (compare bog-trotter).