Apple plans to make notarization a default requirement for all software in the future.
Beginning in macOS 10.14.5, all new or updated kernel extensions and all software from developers new to distributing with Developer ID must be notarized in order to run. In a future version of macOS, notarization will be required by default for all software.Notarization is a new concept introduced in macOS Mojave for apps distributed outside of the Mac App Store with the aim of protecting users from malicious Mac apps.
Mac app developers are encouraged to submit their apps to Apple to be notarized, and an Apple-notarized app includes a more streamlined Gatekeeper dialog to reassure users that an app is not known malware.
Apple provides trusted non Mac App Store developers with Developer IDs that are required to allow the Gatekeeper function on macOS to install non Mac App Store apps without extra warnings, but notarization takes it one step further.
With the new requirement in macOS 10.14.5, developers who are new to distributing Mac apps with a Developer ID will need to go through the notarization process for their apps to work on the Mac.
Apple late last year said that it would begin highlighting notarization status "more prominently" starting in spring 2019, and macOS 10.14.5 is apparently the update where that will begin happening.
The notarization process is designed for non Mac App Store apps and is not required for those that are submitted to the Mac App Store. More information on notarization can be found on Apple's developer site.