In modern times, it has become the standard to tune pianos to A440. The note A above middle C is tuned so that it vibrates at 440 Hz (440 vibrations per second), and all other notes on the piano are tuned in relation to that note. Because A440 is a measurable standard, all pianos in the world can be tuned to the same pitch.
This was not always the case. In the 1950s, the International Organization for Standardization adopted A440 as the standard frequency for the note A above middle C, on pianos and other musical instruments. With this internationally recognized standard pitch, pianos around the world can be tuned so that the same note played on any pair of correctly tuned pianos will sound the same.
Prior to this accepted standard, pianos and other musical instruments had no single common pitch for tuning. Pitch pipes or tuning forks could often vary in pitch by a considerable amount, so that even an untrained musician could hear the difference between two different pianos playing the same note. Instruments played in the same venue would all tune to the same pitch, often to the piano or organ, but the A note on one piano might vibrate at 445 Hz, while the A on a piano in a different town might vibrate at 425 Hz.
With the quality of audio recordings, it is a great benefit to audiophiles that pianos are all tuned to the same note. Attempting to play along with a recorded performance would be painful if the piano on the CD were tuned to a different pitch than the piano in your den. Two pianists who play a duet on different pianos can feel certain that their instruments will sound good together, because all their notes will have the correct pitch.
Tuning a piano is a delicate operation, and requires an experienced piano tuner. Whether using an electric tuner or a simple tuning fork, all the pianos she tunes will have the same pitch, with the standard A440 tuning. From that note, a qualified piano tuner will be able to tune all the rest of the keys by ear, and relying on the standard pitch of the first string, all the pianos will sound the same.