Here's a basic summary of the Mac OS X versions:
10.0 - Cheetah
10.1 - Puma
10.2 - Jaguar
10.3 - Panther
10.4 - Tiger
10.5 - Leopard
10.6 - Snow Leopard
10.7 - Lion
These versions come in numbers 10.x.y. Any updates where the y number changes are free, and any updates where the x number changes cost money.
Basically, if you have 10.4.11 that means you have Tiger, and the printer drivers are not compatible with an older operating system like Tiger. You can upgrade to Leopard, but Leopard costs a lot of money now because it is not made anymore, therefore it is in higher demand. It's almost not worth buying because it's almost $300 for a new Leopard DVD.
If you have an iBook the latest you'll be able to run is Leopard because it's very likely that you have a PowerPC processor (the old processors Apple used to make themselves before they switched to Intel in 2006). Leopard is the last known version of Mac OS X to be compatible with a PPC processor and even then sometimes it lags a good amount and it's occasionally buggy.
HOWEVER, if you go up to the menu bar and click > About This Mac and you have an Intel processor, chances are Snow Leopard can work on your machine. You can buy this also at Amazon for just under $100.
If you have to upgrade the OS to use the printer and you have a PPC, you can buy Leopard for $200-300 on Amazon, or you can buy a new Mac. Expensive, but you get more than what you pay for really.
Hi, and welcome to Apple Support Communities.
Which exact iBook G4 model do you have?
You can choose from this list:
No iBook can run anything newer than Mac OS X 10.5 (Leopard).
See if your iBook meets the system requirements for Leopard here:
Even if the iBook meets the requirements for Leopard, it may be cheaper to buy a compatible printer than it is to buy the full retail version of Mac OS X 10.5 you would need in order to upgrade.
For a history of Mac OS X, you can check out the Wikipedia article on it:
That should alleviate your confusion.