What does the word mon dieu mean in English?

This answer by Hubert Lamontagne is the best written description of how to pronounce ”mon dieu”:

Mon : consonant ‘m’ + vowel ‘on’ (a kind of nasal ‘o’, similar to ‘on’ in ‘don’t’)

Dieu : consonant ‘d’ + consonant ‘y’ + vowel ‘eu’ (a vowel with pursed lips, closest English equivalent would be ‘er’ but it doesn’t have any ‘r’ sound to it… if you know German, it’s the same as ‘ö’).