early 14c., spellen, "read letter by letter, write or say the letters of;" c. 1400, "form words by means of letters," said in most etymology sources to be from Anglo-French espeller, Old French espelir "to mean, signify; explain, interpret," also "spell out letters, pronounce, recite."
This French word is from Frankish *spellon "to tell" or some other Germanic source, from Proto-Germanic *spellam (source also of Dutch spellen, Old High German spellon "to tell," Old Norse spjalla, Gothic spillon "to talk, tell").
The native cognate word is Old English spellian, spillian "to tell, talk, speak, discourse." Only Barnhart seems to allow that the modern English word is partially from the Old English one, due to the difference in sense.
Klein's sources suggest a possible origin for this Germanic group in a PIE root *spel- (2) "to say aloud, recite, speak with emphasis" and cognates in Greek apeilē "threat" among other words, but Beekes finds the suggestion "rather far-fetched."
Also in early use speldren, from Old French espeldre, a variant of espelir. Related: Spelled; spelling.
In early Middle English still "to speak, preach, talk, tell," hence such expressions as hear spell "hear (something) told or talked about," spell the wind "talk in vain" (both 15c.). The meaning "form words with proper letters" is from 1580s.
Spell out "explain step-by-step" is recorded from 1940, American English. Shakespeare has spell (someone) backwards "reverse the character of, explain in a contrary sense, portray with determined negativity."