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.