Leave it to Apple to design a device that you can’t simply hit the on and off button and expect it to turn off. This fact was lost on some people who purchased the iPhone, pressing the power button does not turn the iPhone or iPod Touch completely off.
Instead, pressing the power button (located on the top of the unit) puts both devices in a standby mode where the display is turned off, kind of like a *gasp* computer, but thinking about it they are like tiny computers.
When the iPhone is in its standby mode, it is still accessing the nearest network and updating your emails, messages you have missed and so forth, this is why its possible to run up a $4,000 bill while overseas with the iPhone.
I don’t really know what the iPod Touch does with its standby mode as it doesn’t have SMS or the email application but both devices resume quicker from the standby modes than if they are turned off and have to perform a full boot each time.
Also, with the iPod Touch, shutting down completely and starting up again uses a large amount of battery life so I don’t recommend doing it unless its going to be sitting on a shelf for a while.
If you are traveling overseas, the iPhone will access foreign network if not turned completely off, to turn either the iPhone or iPod Touch off, first if it isn’t on, turn it on then hit the power button at the top of the unit which places it in standby then press and hold the same button for a few seconds until “Slide to turn off” is displayed, slide the slider and it will shut down, a lot like a computer.
Like I said, when you want to turn it back on from being completely off it will take a few seconds to come back on.
This procedure is more important for the iPhone than it is for the iPod Touch.