Introduced in Tiger, the launchd process invokes each script on a schedule specified in a script-specific property list (.plist file) in the /System/Library/LaunchDaemons directory. The specific property list for each script is as follows:
daily script: com.apple.periodic-daily.plist
weekly script: com.apple.periodic-weekly.plist
monthly script: com.apple.periodic-monthly.plist
Additional information about launchd can be found in the Apple Developer Connection document System Startup Programming Topics.
How the timer used by launchd handles sleep time has led many to incorrectly believe that they no longer need to run the maintenance scripts and that the scripts are run automatically if the Mac was asleep or shutdown at the scheduled time.
While it may appear that launchd executes the maintenance scripts "on the fly" if the computer is asleep or shutdown at the appointed time, this is a side effect of how the timer treats the time the computer has spent in sleep mode. The timer used by launchd does not count sleep time. If your Mac is asleep at the scheduled time when a given script is supposed to run, the script may run later that day at a time shifted by the amount of time the Mac was asleep. However, if you restart your Mac before the time-shifted execution time, pending events are lost and the script will not run off-schedule: the next chance for the script to run will be at its regularly scheduled time.
If you regularly restart your Mac and the computer regularly sleeps or is shut down at the scheduled times, it's possible that the scripts will never run, hence one should still run them manually, such as on a weekly basis.