I have an iMac OS High Sierra that I bought in July 2012. Do I understand correctly that I can not upgrade it any longer?

Hi Debra, I still use a 2011 iMac running 10.13.6 & feel fairly safe because I don't use FaceBook, Twitter & other such things.

The latest OS requires...

macOS Big Sur - Technical Specifications

General Requirements

• OS X 10.9 or later
• 4GB of memory
• 35.5GB available storage on macOS Sierra or later*
• Some features require an Apple ID; terms apply.
• Some features require a compatible internet service provider; fees may apply.

Mac Hardware Requirements

For details about your Mac model, click the Apple icon at the top left of your screen and choose About This Mac. These Mac models are compatible with macOS Big Sur:

• MacBook (2015 or later)
• MacBook Air (2013 or later)
• MacBook Pro (Late 2013 or later)
• Mac mini (2014 or later)
• iMac (2014 or later)
• iMac Pro (2017 or later)
• Mac Pro (2013 or later)

Learn about compatibility and how to identify your specific Mac model

The Prevoius OS may work if it's a Late 2012 iMac...

macOS Catalina - Technical Specifications

General Requirements

• OS X 10.9 or later
• 4GB of memory
• 12.5GB of available storage (OS X El Capitan 10.11.5 or later)*
• Some features require an Apple ID; terms apply.
• Some features require a compatible internet service provider; fees may apply.

Mac Hardware Requirements

For details about your Mac model, click the Apple icon at the top left of your screen and choose About This Mac. These Mac models are compatible with macOS Catalina:

• MacBook (Early 2015 or newer)
• MacBook Air (Mid 2012 or newer)
• MacBook Pro (Mid 2012 or newer)
• Mac mini (Late 2012 or newer)
• iMac (Late 2012 or newer)
• iMac Pro (2017)
• Mac Pro (Late 2013 or newer)

https://support.apple.com/en-us/HT210190

https://apps.apple.com/gb/app/macos-catalina/id1466841314?ls=1&mt=12

How to upgrade to macOS Catalina – Apple Support

And caution on 10.15 or higher, to see which Apps will no longer work in 10.15 get Go64...

https://www.stclairsoft.com/Go64/

Then there is Mojave, that I'm using on my 2019 iMac because it's the last OS that supports 32 Bit Apps...

https://support.apple.com/kb/SP777?locale=en_US

https://itunes.apple.com/us/app/macos-mojave/id1398502828?mt=12

Don't use FireFox for these links…