Apple updates the Mac operating system on a yearly basis.  In years past, it was not always easy to find installers for previous versions of macOS. Today, however, it is quite simple to download older version of the macOS whether through third party applications or from Apple itself.

Apple’s website has a page on how to download and install macOS. This page contains links for operating systems as far back as macOS High Sierra (10.13) using the Mac App Store. For versions of the Mac operating system from macOS Sierra (10.12) back to macOS Lion (10.7), web links are provided. The page also contains instructions on downloading macOS using the Terminal, creating and using bootable installers and checking compatibility of Mac computers with the Mac operating system.

If you want to get more granular and download not only older versions of the macOS but also particular updates, a Mac application called Mist makes this straightforward. OSXDaily has a page with instructions on downloading and using Mist.

If you are searching for versions of Mac OS X prior to 10.7, you are entering the world of vintage computing. Mac OS X Lion (10.7) was the first version of the Mac operating system released for electronic download. Versions prior to 10.7 were released on CD-ROM or floppy disks.  

Apple officially supports the three most recent versions of the Mac operating system. This means that security updates are still released for these versions. Versions of macOS older than this no longer receive updates including security updates. With the proliferation of online threats, one should not use unsupported versions of the macOS for anything where privacy and security is a concern.