Yes, you can upgrade.
Depending on the Processor speed, you can upgrade to OS X 10.4.11
If your processor is faster than 867 MHz, then you can upgrade to OS X 10.5.x
Either of those require you to purchase that upgrade, as there are no free downloads to do that.
How much RAM memory is installed in your iMac? If you upgrade your operating system, it will be a good idea to consider also increasing the RAM that you have installed.