10.4.11 is Tiger.
If yours is a PPC based Mac (a G4 or G5) you can upgrade to Leopard 10.5.8 but no further. Leopard is no longer supported by or available from Apple so you will need to buy a vlack retail install disk from eBay or Amazon, and they cost around $200.
If yours is an Intel based Mac you can bypass Leopard and go straight to Snow Leopard 10.6.8:
Start by checking if you can run Snow Leopard:
Requirements for OS X 10.6 'Snow Leopard'
The OS 10.6 Snow Leopard install DVD is available for $19.99 from the Apple Store:
and in the UK:
When you have installed it, run Software Update to download and install the latest updates for Snow Leopard to bring it up to 10.6.8, or download the combo update from here:
Check via Software Update whether further updates are required.
You can determine what kind of iMac you have by clicking the Apple icon top left of your finder window, then on About this Mac.
So we know more about it...
At the Apple Icon at top left>About this Mac, then click on More Info, then click on Hardware> and report this upto but not including the Serial#...
Model Name: iMac
Model Identifier: iMac7,1
Processor Name: Intel Core 2 Duo
Processor Speed: 2.4 GHz
Number Of Processors: 1
Total Number Of Cores: 2
L2 Cache: 4 MB
Memory: 6 GB
Bus Speed: 800 MHz
Boot ROM Version: IM71.007A.B03
SMC Version (system): 1.21f4
PS. All OSX versions & names...