TUAW has an excellent article on the new Safe Sleep feature found in the October 2005 PowerBooks

With the latest iteration of PowerBooks Apple just released, a new feature called Safe Sleep was introduced that Fabienne covered a couple weeks ago. In case you missed it, the short of the long of this handy new feature is that it works like the Hibernate feature of Windows: you can save a snapshot of what you're working on to your hard drive and completely power down the notebook - meaning you can swap out batteries and power back up to your desktop as you left it in about 10 seconds, or simply store the notebook without draining any power, like the regular Sleep feature does.

Click through to the TUAW article to find out about how to enable Safe Sleep on any PowerBook.

Safe Sleep was introduced in Power Manager 2.0 and is covered in Apple's Technical Note TN1190

This form of sleep is similar to simple sleep, but a file is written to disk that represents the contents of memory at the point of sleeping so that -- should an unexpected loss of power occur -- the user's working context can be fully restored upon the next startup. Currently, this variation of sleep is only available if Virtual Memory is turned on in the Memory Control Panel. Safe sleep is enabled if the user checks the "Preserve memory contents on sleep" checkbox in the Advanced Settings panel of the Energy Saver Control Panel.

Apple Knowledge Base Article 302477 discusses the progress bar that appears after waking from sleep on the PowerBook G4 (Double-Layer SD).

The progress bar indicates that the PowerBook is waking from Safe Sleep. Safe Sleep ensures that data stored in main memory will not be lost should the system shut down due to a loss of power during sleep mode. Prior to your system entering sleep, Safe Sleep automatically saves the contents of main memory—such as desktop settings, open applications, and other work in progress—to the hard drive. In the event the battery becomes completely depleted while the system is asleep, the computer will shut down. But when a power adapter is connected or a freshly charged battery is installed, the PowerBook can be restarted and it will automatically return to the desktop state that existed prior to entering sleep. This means that applications and files will remain exactly as they were prior to the system being put to sleep, making it easy for you to continue on with your work.