What do these numbers mean on Mac?
I am on an iMac running Catalina.
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The number on App Store icon indicates the number of available app updates. The number on the System Preferences icon depends on what option in System Preferences also shows the number. Often it is that there is a software update to macOS available.
In some apps, it's the number of notifications: like email, or messages.
The launcher you see towards the bottom of your Mac is called the Dock, a prominent part of macOS user experience. You can learn more about the Dock in macOS here
The red circle you see on an app icon is called a Badge. Quoting from the macOS Human Interface Guidelines - Badging section:
Apps can display a small red oval containing a white number on their Dock icon to indicate when new interesting—but noncritical—information is available. For example, App Store uses badging to indicate the number of available app updates; when there are no updates available, the badge disappears.