early 14c., "make illustrious, glorify, make known" (a sense now obsolete), from Old French clarifiier "clarify, make clear, explain" (12c.), from Late Latin clarificare "to glorify," literally "to make clear," from Latin clarificus "brilliant," from clarus "clear, distinct" (see clear (adj.)) + combining form of facere "to make, to do" (from PIE root *dhe- "to set, put").
Meaning "make clear, purify" (especially of liquors) is from early 15c. in English. Figurative sense of "to free from obscurity, render intelligible" is from 1823. Intransitive sense of "grow or become clear" is from 1590s. Related: Clarified; clarifying.