Answer + Explanation:
ME would mean that the provenance (where it originally came from) of an English word would have been handed down to us from Middle English. I suspect that were you to scan, say, a poem in ME, you would hardly believe it had ever been English.
This notation indicates the origin of the word — that is, what language that word came into the English from. Any dictionary that gives a word’s etymology will include these kinds of notations.