A440 is the 440 Hz tone that serves as the internationally recognized standard for musical pitch. A440 is the musical note A above middle C. Since 1939, it has served as the audio frequency reference for the calibration of pianos, violins, and other musical instruments.
Tuning a piano is an example of a simple frequency calibration that is actually done with the human ear. The piano tuner listens to a standard musical pitch and compares it to the same note on the piano keyboard. The piano is then adjusted (by tightening or loosening strings), until it agrees with the audio standard.
The smallest frequency offset that a piano tuner can hear depends on lots of factors, including the sound volume, the duration of the tone, the suddenness of the frequency change, and the musical training of the listener. However, the just noticeable difference is often defined as 5 cents, where 1 cent is 1/100 of the ratio between two adjacent tones on the piano's keyboard.