This refers to the International Pitch Standard, where the note A above middle C is taken as 440Hz. This was added to the Marine Band years ago to make it clear that this was a serious instrument, tuned to International Concert Pitch, as opposed to the various harmonicas that were produced back then, tuned to Continental Pitch (somewhat flatter at A=435Hz). Strictly speaking, it means that the keynote of the harmonica (the note you get when you blow into hole 1) is tuned relative to 12 Tone Equal Temperament at A=440Hz. As the Marine Band has generally been tuned in Just Intonation, or a light temperament rather than 12TET, the various A notes on harps of different keys may be slightly higher or slightly lower than 440Hz, but the key notes of the various harps should match up with the corresponding notes on a piano keyboard. (For more on the topic of temperament, along with some audio examples, you may want to go here.)
However, it should be noted that concert pitch in many countries is now often slightly higher than A=440Hz and as harps also tend to flatten in pitch when they are played with increasing pressure, most harmonica manufacturers tune them slightly sharp. Currently, Marine Bands seem to be tuned relative to something like A=443Hz and as of some time in 2012, the A440 stamp has been dropped from their covers.
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