1939, popularized in World War II army slang, from walk (v.) + talk (v.).
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walk v.
"travel on foot," c. 1200, a merger of two verbs, 1. Old English wealcan "to toss, roll, move round" (past tense weolc, past participle wealcen), and 2. wealcian "to roll up, curl," from Proto-Germanic *welk- (source also of Old Norse valka "to drag about," Danish valke "to full" (cloth), Middle Dutch walken "to knead, press, full" (cloth), Old High German walchan "to knead," German walken "to full"), perhaps ultimately from PIE root *wel- (3) "to turn, revolve."
The shift in sense is perhaps from a colloquial use of the Old English word or via the sense of "to full cloth" (by treading on it), though this sense does not appear until after the change in meaning. In 13c. it is used of snakes and the passage of time, and in 15c. of wheeled carts. "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.; meaning "to escort (someone) in a walk" is from 1620s. Meaning "move (a heavy object) by turning and shoving it in a manner suggesting walking" is by 1890. To walk it off, of an injury, etc., is from 1741. Related: Walked; walking.
talk v.
c. 1200, talken, probably a diminutive or frequentative form related to Middle English tale "story," and ultimately from the same source as tale (q.v.), with rare English formative -k (compare hark from hear, stalk from steal, smirk from smile) and replacing that word as a verb. East Frisian has talken "to talk, chatter, whisper." Related: Talked; talking.
To talk (something) up "discuss in order to promote" is from 1722. To talk shop is from 1854. To talk turkey is from 1824, supposedly from an elaborate joke about a swindled Indian.
Phrase talking head is by 1966 in the jargon of television production, "an in-tight closeup of a human head talking on television." In reference to a person who habitually appears on television in talking-head shots (usually a news anchor), by 1970. The phrase is used earlier, in reference to the well-known magic trick (such as Señor Wences's talking head-in-the-box "Pedro" on the "Ed Sullivan Show"), and to actual talking heads in mythology around the world (Orpheus, Bran).