Old English hunigcamb; see honey (n.) + comb (n.). This use of the Germanic "comb" word seems to be peculiar to English, and the likeness is not obvious. Perhaps the image is from the comb used in wool-combing, but that extended sense of comb is not attested before Middle English. In other Germanic languages the word for it is "honey-string," "honey-cake," "bee-wafer," etc. Latin has favus, Greek melikerion.
Transferred use, in reference to various structures resembling honeycomb, is from 1520s. As a verb, from 1620s (implied in honeycombed).