The notes we play correspond to frequencies, which we measure with the term Hz (hertz)--number of vibrations per second. So when we say "A 440" we're referring to the note A which is tuned to 440 vibrations per second. An issue we've been facing for at least a couple hundred years is the raising of the pitch standard. In Bach's time, the tuning was as much as a half step lower. So the note A, on an instrument or notated on sheet music, would have sounded like an Ab in Bach's time.
If you hear a modern European orchestra, the A can be as high as 445, maybe higher. The strings like to tune high because they sound more brilliant, and I imagine the conductors like it as well. Yet, there's a big interest in lower tunings today, particularly the A=432 tuning. Many listeners feel the music sounds better when the pitch is lowered. There are even apps you can download that play the songs in your library at 432, so you can check that out and see what you think.
I do notice that animal and bird sounds (I live in the country) are tuned closer to 432 than 440. I practice outside every day so I notice this.
As musicians, we need to pay attention to tuning not just for the obvious reason of striving for good intonation, but also because we are the arbiters of frequencies. I'll go into this more in a follow up post.