Since 2004, you could connect an AirPort Express (not Extreme) to an amplifier or self-powered speakers, and play music wirelessly using iTunes (and from any application or web site if you install Rogue Amoeba’s Airfoil software). Apple called this AirTunes.
Then the Apple TV came along and Apple added video, and AirTunes became AirPlay — now you can wirelessly play video from many iOS and Mac apps, and you can display your whole Mac screen if you’re using a recent-vintage Mac with Mountain Lion.
But the exciting thing about AirPlay is that you no longer need an Airport Extreme or Apple TV to use it for wireless music, because Apple has licensed AirPlay to third-party vendors such as Bose, JBL and Logitech. This means you can now buy powered speakers with built-in AirPlay that you can put anywhere in your house, and play music from them from any iOS device or computer. These speakers join your Wi-Fi network, and you can have as many as you want — it’s like attaching an invisible cable from any device to any AirPlay speakers you have, whenever you need it.
I like this solution much better than the Bluetooth speakers such as those made by Jawbone. Bluetooth requires that the device or computer sending audio be be in close physical proximity to the speakers, and that every device or computer go through a sometimes cumbersome “pairing” process. While this can be ok in a small apartment with one or two devices, AirPlay isn’t limited in this way; as long as the speakers are on the same Wi-Fi network, you’re set. Also, AirPlay audio should be as good as wired audio, whereas Bluetooth audio is compressed, and so inherently worse.
Receiver manufacturers such as Pioneer and Denon are also building AirPlay into their products — they’ll automatically switch the input if you start sending it music from your device or computer.
If you prefer your own pair of speakers that don’t feature AirPlay capability, but you don’t want to have a whole receiver involved, you can still get an AirPort Express and plug it into powered speakers (I use this setup with a pair of AudioEngine 2 speakers at my desk). Or, if your speakers are unpowered, you can buy mini-amplifiers just for this purpose, such as the AudioEngine N22 or the Griffin Technology Twenty. I imagine there will soon be versions of these mini-amps with AirPlay technology built in so you won’t even need an AirPort Express.