A440

Refers to the exact pitch, an A, that a modern orchestra aspires to tune its instruments to. The 440 is for 440Hz, which (in my limited understanding of physics) is the frequency at which this particular sound wave oscillates. While this is sort of the standard A these days, A is recognizable over a wide range of frequencies. For a nice list of different historical As see http://www.uk-piano.org/history/pitch.html.

The frequency of the middle A note on a piano (that's the one above, i.e. further to the right, of middle C).

This hasn't always been the case, and there are still, in fact, exceptions, most notably in Baroque music. Through the years the frequency of A has ranged from about 390 Hertz to 460 Hz. A higher A is sometimes used in an attempt to give the instruments a "brighter" sound. Tuning an instrument higher can have the adverse effect of causing more broken strings, especially in the days when they were made of gut.

The next higher A would have a frequency of 880, then 1760, and so on.

In music, A 440 is known as the a above middle C, and vibrates at 440 cycles per second (440 hertz). Because it is just above the bass clef, A 440 is a good note for tuning musical instruments, since almost all instruments have 440 hz within their native range. When a symphony orchestra performs, the concertmaster will direct the oboe to sound the A, and the other instruments will tune to it. A 440 is usually sounded twice before a performance, and the instruments play a sort of 'humming' sound as they compare their tune to that of the oboe. Once in tune, the concertmaster will sit and the conductor will take the stage so the music may begin.