Are your displays "mirrored," meaning, are they showing the same thing? If so, then no, you can't display two different background images, because the displays are supposed to display the same thing.
If you're running an "extended desktop," meaning, you can slide your mouse pointer from one display to the next -- kind of like one, big monitor, then it's very simple: open System Preferences, click on "Desktop & Screen Saver" and then click the "Desktop" tab. One window should be open on each monitor -- one should display both the "Desktop" and "Screen Saver" tabs, while the other should only display the currently selected tab on the main monitor. Choose a different background for each monitor until your heart's content.
Again, if you're mirroring your displays, then you are showing identical images on each monitor, and therefore, they will display the exact same thing (you cannot change the desktop on one and not the other). If you're using extended desktop mode, then just open System Prefs and change away.
Also, your signature says you're using an iBook, and I assume this is the machine you're doing it with. The iBook does not support extended desktop mode, so you'll be stuck with mirrored mode, meaning you cannot use your external monitor as an extended desktop monitor -- it MUST be mirrored.
There are hacks out there that will allow you to use extended desktop mode, but I don't know if they've been tested with the iBook G4 and I would not recommend using them. Reply back if you're still interested and I'll look up some links.