span (n.1)
"distance between two objects," from Old English span "distance between the thumb and little finger of an extended hand" (as a measure of length, roughly nine inches), probably related to Middle Dutch spannen "to join, fasten," from Proto-Germanic *spannan, from PIE root *(s)pen- "to draw, stretch, spin."

The Germanic word was borrowed into Medieval Latin as spannus, hence Italian spanna, Old French espan "hand's width, span as a unit of measure," French empan. As a measure of volume (early 14c.), "what can be held in two cupped hands." Meaning "length of time" first attested 1590s; that of "space between abutments of an arch, etc." is from 1725. Meaning "maximum lateral dimension of an aircraft" is first recorded 1909.
span (v.)
Old English spannan "to join, link, clasp, fasten, bind, connect; stretch, span," from Proto-Germanic *spannan (source also of Old Norse spenna, Old Frisian spanna, Middle Dutch spannen, Dutch spannan "stretch, bend, hoist, hitch," Old High German spannan, German spannen "to join, fasten, extend, connect"), from PIE root *(s)pen- "to draw, stretch, spin" (source also of spin (v.)).

The meaning "to encircle with the hand(s)" is from 1781; in the sense of "to form an arch over (something)" it is first recorded 1630s. Related: Spanned; spanning.
span (n.2)
"two animals driven together," 1769, American English, from Dutch span, from spannen "to stretch or yoke," from Middle Dutch spannan, cognate with Old English spannan "to join," from Proto-Germanic *spannan, from PIE root *(s)pen- "to draw, stretch, spin." Also used in South African English.