Explain
late Middle English: from Latin explanare, based on planus ‘plain’.
wiktionary
From Middle English explanen, from Old French explaner, from Latin explanō(“I flatten, spread out, make plain or clear, explain”), from ex-(“out”) + planō(“I flatten, make level”), from planus(“level, plain”); see plain and plane. Compare esplanade, splanade. Displaced Old English ġereċċan.
etymonline
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.