walk (v.) Look up walk at Dictionary.com
Old English wealcan "to toss, roll," and wealcian "to roll up, curl, muffle up," from Proto-Germanic *welk- (cf. Old Norse valka "to drag about," Danish valke "to full," Middle Dutch walken "to knead, press, full," Old High German walchan "to knead," German walken "to full"), perhaps ultimately from PIE root *wel- "to turn, bend, twist, roll" (see vulva).

Meaning shifted in early Middle English, perhaps from colloquial use of the Old English word. "Rarely is there so specific a word as NE walk, clearly distinguished from both go and run" [Buck]. Meaning "to go away" is recorded from mid-15c. Transitive meaning "to exercise a dog (or horse)" is from late 15c. The surname Walker probably preserves the cloth-fulling sense. Related: Walked; walking.
walk (n.) Look up walk at Dictionary.com
late 14c., "act of walking" (see walk (v.)). The noun meaning "broad path in a garden" is from 1530s; walk of life is from 1752. Sports sense of "base on balls" is recorded from 1905. To win in a walk (1854) is from horse racing.