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Not arrogant, aog, I hope, but conscious that you may be feigning ignorance. But, nonetheless, here goes: the primary use and meaning of 'mere' and its adverb 'merely' is to describe something as no more and no less than as designated, as described.
'A mere private,he rose to general' means that he was an ordinary private, with nothing to mark him out as, for example, having political influence, wealth, genius or, of course, exceptional bravery. 'Mere' is here used for the sake of the contrast, to point up the ordinariness of the man
And a medal for those 'who merely served' is one given to all who served; those who are ordinary servicemen or women, no more, no less, as designated; just for serving, in contrast to the other medal which is only given to those who display exceptional bravery when they served..