For many years macOS has included a technology called Gatekeeper that is designed to ensure that only trusted software runs on your Mac. By default the security and privacy preferences of your Mac are set to allow applications from the App Store and identified developers, this will allow you to install or run applications from identified developers without any issues.
For additional security, you can choose to allow only applications from the App Store. But this does limit your options when installing applications outside of the App Store.
If your Mac is set to only allow applications from the App Store, you will need to change the preference to allow applications from the App Store and identified developers.
If your Mac is set to allow applications from the App Store and identified developers, the first time that you launch a new application, your Mac will ask you if you are sure you want to open it.
This has changed with macOS Catalina and macOS Big Sur where all applications outside of the App Store need to be notarized.
Opening a developer-signed application that has not been notarized or the notarization has failed
Prior to Catalina an application outside of the App Store only required signing using an identified developer certificate. When you opened an application that was not notarized, you are shown a yellow warning icon and asked if you're sure you want to open it.
From Catalina onwards if your Mac is set to allow applications from the App Store and identified developers, and you try to install an application that is not notarized by Apple, you will see a warning that the app cannot be opened because Apple could not scan the app for known malicious software.
If there is not an update that offers notarization but the application is still signed and is from a trustworthy source - so that you can be sure it has not been tampered with - you can temporarily override your Mac security settings to open it.
When an app fails to install because it has not been notarized or is from an unidentified developer, it will appear in System Preferences in the section Security & Privacy, under the General tab. In this section you can click Open Anyway to confirm your intent to open or install the application.
After clicking on Open Anyway a warning prompt will reappear so that you can click Open to run the application or installer.
The application will be saved as an exception to your security settings, and running the application in the future will not require any confirmation, just as if it was a notarized application.