What does each letter of the word monarch mean?

There is no meaning to any of the letters. The letters in the English alphabet do not have meanings. Only the Words that are made up of them do.

The individual letters in a Word don't mean anything. By themselves, they simply indicate what sound you're supposed to make. For example, the letter "s" indicates the s sound (which sounds like "ssssss").

The exception to this is acronyms. Acronyms are Words made up of the first letter of each Word in a phrase. For example, "Scuba" is an acronym meaning, "self-contained underwater breathing apparatus."

Most Words are not acronyms, so their letters have no meaning.