Correct spelling, explanation: message is the correct spelling because the word comes from the French message, so from a word of the exact same spelling. Nevertheless, the French version comes from the Latin missus. Message is therefore the correct form. At first, the word had only the meaning of divine communication, but it got a broader meaning around the 18th century. Other spellings, like mesage are mistaken.

Definition of message:
noun, a communication sent or left for someone; also: an important idea behind a speech, piece of art, film, etc.
Mr. Jones is not in his office but you can leave a message.
This book gives an important message on tolerance and humanity.

Incorrect spelling, explanation: mesage is incorrect, the word should be written with double s, as in message, due to exactly the same spelling in the original French message and double s in the earlier Latin missus. Therefore the correct spelling is message.

Incorrect spelling

Incorrect spelling