I would like to update my iMac software. Can this be done?

The model year of an iMac is available at Apple menu > About This Mac.

A late-2009 through mid-2011 iMac can be upgraded to High Sierra 10.13.6 but no later version.

A late-2012 through late-2013 iMac can be upgraded to Catalina 10.15.7. See: https://support.apple.com/en-us/HT211683

A mid-2014 or later can be upgraded to the current version of Big Sur. See: https://support.apple.com/en-us/HT201475

Your upgrade path is inexorably tied to your iMac sub-model, which we do to know. Older Mac have limitations on the highest OS version they can run.

Please do "About this Mac..." from your Apple menu and tell us what the shows for SUB-MODEL:

⚠️ For security reasons, please DO NOT post a serial number here.

Maybe. It is called an upgrade. That is when you install a newer OS than the one you are using. An update is when you install a newer version of the same OS. Links to these upgrades are found on Apple's help site as well as in the Apple App store. If you tell us what year and model Mac you are using, plus the operating system it has, then someone here can advise you whether it can be upgraded and to what OS. Otherwise, since our psychic is on vacation this week, we don't know what you have. Also, be aware that some upgrades can result in some older 32 bit apps no longer working, so you should address this issue.