When a string on a piano is struck it vibrates back and forth. The faster it vibrates, the higher the sound. The slower it vibrates the lower the sound will be. The lowest note on the piano vibrates about 27.5 times a second and the highest about 3520 times a second. The number of vibrations per second is called cycles or Hertz and is also the frequency of the tone. Sometimes you will hear this referred to as the 'pitch'.
The "A" stands for the A (or the ninth key) above middle C. The 440 refers to the sound frequency of 440 vibrations per second. This means that when the A above middle C is tuned to 440, that string is vibrating back and forth 440 times a second.
Most technicians tune the first A at 440 using a tuning fork, or electronic device, and then they tune the rest of the piano to this note.