Old English fæðm "length of the outstretched arm" (a measure of about six feet), also "arms, grasp, embrace," and, figuratively "power," from Proto-Germanic *fathmaz "embrace" (source also of Old Norse faðmr "embrace, bosom," Old Saxon fathmos "the outstretched arms," Dutch vadem "a measure of six feet"), from PIE *pot(ə)-mo-, suffixed form of root *pete- "to spread." It has apparent cognates in Old Frisian fethem, German faden "thread," which OED explains by reference to "spreading out." As a unit of measure, in an early gloss it appears for Latin passus, which was about 5 feet.
Old English fæðmian "to embrace, surround, envelop," from a Proto-Germanic verb derived from the source of fathom (n.); cognates: Old High German fademon, Old Norse faþma. The meaning "take soundings" is from c. 1600; its figurative sense of "get to the bottom of, penetrate with the mind, understand" is from 1620s. Related: Fathomed; fathoming.