Sound occurs when air is set into motion rapidly. Humans can hear sound if those cycles of compression and uncompression occur anywhere from twenty times each second to about twenty thousand times each second.
When a piano string is set into motion, it vibrates up and down repeatedly. If the note A above middle C is properly tuned, that string will vibrate up and down 440 times in one second. That's what A-440 means.
Every note on a piano is tuned using A-440 as the starting point. A-440 has been accepted as the universal standard for most of the century. Before that, it varied as much as a semi-tone higher or lower.
And even further back in time, there was no standard at all. Every village used a prominent local instrument, such as a church organ, as the standard for tuning its musical instruments. Pity the wandering minstrel!
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