What is the function of the power button on the Apple Wireless Keyboard?

The power button only powers ON/OFF the keyboard, it doesn’t power off the computer.

To power off your computer using the keyboard, you might want to use any of the following:

Reference:

• ⌘ (Command key) - On some Apple keyboards, this key also has an Apple logo ()
• ⌃ (Control key)
• ⌥ (Option key) - "Alt" may also appear on this key
• ⏏ (Eject)
• ⇧ (Shift)

⌃ Control + ⏏ Eject : Show shutdown dialog

⌥ Option + ⌘ Command + ⏏ Eject : Put the computer to sleep

⌃ Control + ⌘ Command + ⏏ Eject : Quit all applications (after giving you a chance to save changes to open documents), then restart the computer.

⌃ Control + ⌥ Option + ⌘ Command + ⏏ Eject : Quit all applications (after giving you a chance to save changes to open documents), then shut down the computer.

⇧ Shift + ⌃ Control + ⏏ Eject : Sleep the display, but not the computer. (thanks to VxJasonxV)

Is the power button strictly limited to turning on and off the keyboard itself?

Yep. The wireless keyboard software detects inactivity and will go in sleep mode where it reduces power consumption, however it's probably better to turn it off if you know you won't be using it for a while. You must press that button for a few seconds. The light will show, then it will disappear while you are still holding the button. Then you know it is off.

When you turn it off that way it should display a notification on the OS X desktop, that the bluetooth device was turned off.

I'm not using one anymore. When I did, I would often forget to switch off the keyboard.

Now that I think of it it would be nice if there was an option for the computer to tell the keyboard to power off. That way when you shut down your Mac it would power off. I don't remember seeing such an option :(