macOS could not be installed on your computer

If you are using System Preferences> Software Update to download the Security Update, but for some reason you have selected the Upgrade Now button for macOS Catalina.

Anyway forget Software Update and download the Security Update manually from here.

https://support.apple.com/kb/DL2042?viewlocale=en_US&locale=en_US

Once downloaded double-click to install.

Phil, you are posted in the macOS forum. Your profile does not indicate your are running Mojave which is why I asked. The image you posted contains the background picture for Catalina, thus, the reason I thought that was what you were running.

You can re-open Software Update and click on the more info link to show the available updates. Be sure to uncheck Catalina if you do not wish to upgrade.

The update can be downloaded here: Download Security Update 2020-003 (Mojave). This is a direct download. There are prior security updates for Mojave that may have to be installed before you can install this one. It is not clear as to why you got the error when trying to install the update. Before going further, I suggest you do the following:

Repair the Drive for El Capitan or Later

1. Restart the computer. Immediately, at or before the chime, hold down the Command and R keys until the Apple logo and progress bar appear. Wait until the Utility Menu appears.
2. Select Disk Utility and press the Continue button.
3. Then select the indented (usually, Macintosh HD) volume entry from the side list. 
4. Click on the First Aid button in the toolbar and wait for the Done button to activate. Click on it, then quit Disk Utility.
5. Select Restart from the Apple menu.

Another thing you could also do after the above is: Download and Install the macOS Mojave 10.14.6 Combo Update.

There is no security update for Catalina. There is a Supplemental Update for Catalina. In order to address your question, you need to provide more information such as the version of macOS currently installed on your computer, the exact computer model you have, and the full name of the update you are trying to install.

Please read Writing an effective Apple Support Communities question. We are here to help. We are all users. We are not mind-readers nor clairvoyants. We only know what you write down and tell us. Be specific and thorough. Include your hardware information and installed version of macOS. Try to write clearly. Think about what you want to say before you write it down, then re-read it to see if it makes sense.

FYI: These are user-only forums. This is not Apple Support. if you need to contact Apple Support, then contact product and tech support:  Contacting Apple for support and service including international calling numbers.

These forums only provide help with Apple products. Thank you for your understanding and support.

That update is for Mojave. Are you running Mojave or Catalina? The update will not work with Catalina.