"to explain, as a man to a woman, in a way that she feels insults or ignores her intelligence and experience in the matter," by 2008, from man (n.) + second element from explain (v.). The form 'splain, as a clip of explain, had been used at least since the 1960s as a colloquialism. Related: Mansplained; mansplaining.
Entries linking to mansplain
"a featherless plantigrade biped mammal of the genus Homo" [Century Dictionary], Old English man, mann "human being, person (male or female); brave man, hero;" also "servant, vassal, adult male considered as under the control of another person," from Proto-Germanic *mann- (source also of Old Saxon, Swedish, Dutch, Old High German man, Old Frisian mon, German Mann, Old Norse maðr, Danish mand, Gothic manna "man"), from PIE root *man- (1) "man." For the plural, see men.
Sometimes connected to root *men- (1) "to think," which would make the ground sense of man "one who has intelligence," but not all linguists accept this. Liberman, for instance, writes, "Most probably man 'human being' is a secularized divine name" from Mannus [Tacitus, "Germania," chap. 2], "believed to be the progenitor of the human race."
Specific sense of "adult male of the human race" (distinguished from a woman or boy) is by late Old English (c. 1000); Old English used wer and wif to distinguish the sexes, but wer began to disappear late 13c. and was replaced by man. Universal sense of the word remains in mankind and manslaughter. Similarly, Latin had homo "human being" and vir "adult male human being," but they merged in Vulgar Latin, with homo extended to both senses. A like evolution took place in Slavic languages, and in some of them the word has narrowed to mean "husband." PIE had two other "man" roots: *uiHro "freeman" (source of Sanskrit vira-, Lithuanian vyras, Latin vir, Old Irish fer, Gothic wair; see *wi-ro-) and *hner "man," a title more of honor than *uiHro (source of Sanskrit nar-, Armenian ayr, Welsh ner, Greek anēr; see *ner- (2)).
Man also was in Old English as an indefinite pronoun, "one, people, they." It was used generically for "the human race, mankind" by c. 1200. As a word of familiar address, originally often implying impatience, c.1400; hence probably its use as an interjection of surprise or emphasis, since Middle English but especially popular from early 20c.
As "a woman's lover," by mid-14c. As "adult male possessing manly qualities in an eminent degree," from 14c. Man's man, one whose qualities are appreciated by other men, is by 1873. Colloquial use of the Man for "the boss" is by 1918. To be man or mouse "be brave or be timid" is from 1540s. Meaning "piece with which a game (especially chess) is played" is from c. 1400.
Man-about-town "man of the leisure class who frequents clubs, theaters, and other social resorts" is from 1734. Man of the world is from mid-14c. as "secular man, layman;" by early 15c. as "man experienced in the ways of the world, one able to take things in stride." To do something as one man "unanimously" is from late 14c.
So I am as he that seythe, 'Come hyddr John, my man.' 
MANTRAP, a woman's commodity. [Grose, "Dictionary of the Vulgar Tongue," London, 1785]
At the kinges court, my brother, Ech man for himself. [Chaucer, "Knight's Tale," c. 1386]
early 15c., explanen, "make (something) clear in the mind, to make intelligible," from Latin explanare "to explain, make clear, make plain," etymologically "make level, flatten out," from ex "out" (see ex-) + planus "flat" (from PIE root *pele- (2) "flat; to spread").
The spelling was altered by influence of plain. Also see plane (v.2). In 17c., occasionally used more literally, of the unfolding of material things: Evelyn has buds that "explain into leaves" ["Sylva, or, A discourse of forest-trees, and the propagation of timber in His Majesties dominions," 1664]. Related: Explained; explaining; explains. To explain (something) away "to deprive of significance by explanation, nullify or get rid of the apparent import of," generally with an adverse implication, is from 1709.