Etymology
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explain (v.)

early 15c., explanen, "make (something) clear in the mind, to make intelligible," from Latin explanare "to explain, make clear, make plain," literally "make level, flatten," 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.

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Definitions of explain

explain (v.)
make plain and comprehensible;
He explained the laws of physics to his students
Synonyms: explicate
explain (v.)
define;
The committee explained their plan for fund-raising to the Dean
explain (v.)
serve as a reason or cause or justification of;
Her recent divorce may explain her reluctance to date again
Synonyms: excuse
From wordnet.princeton.edu