"Meh" is an interjection used as an expression of indifference or boredom. It may also mean "be it as it may". It is often regarded as a verbal shrug of the shoulders. The use of the term "meh" shows that the speaker is apathetic, uninterested, or indifferent to the question or subject at hand. It is occasionally used as an adjective, meaning something is mediocre or unremarkable.
The French loanword ennui comes from the very same Late Latin word that gave us annoy — inodiare ("to make loathsome"). We borrowed ennui several centuries after absorbing annoy into the language. Ennui deals more with boredom than irritation - and a somewhat specific sort of boredom at that. It generally refers to the feeling of jadedness that can result from living a life of too much ease. The poet Charles Lloyd described it well in his 1823 Stanzas to Ennui when he referred to that world-weary sensation as a "soul-destroying fiend" which visits with its "pale unrest / The chambers of the human breast / Where too much happiness hath fixed its home."