What is updated by "a software update is required to connect to <phone>"?

That Apple page reads, in part:

If your iPhone, iPad, or iPod touch has a newer version of iOS than is supported by your Mac, you may see this alert: "A software update is required to connect to your iOS device. Would you like to download and install this update now?"

Click Install to download and install the software so your Mac can update or sync your iOS device. If you continue to see this alert, make sure that your software on your Mac and iTunes are up-to-date.

All this does is install software on your Mac which allows macOS (usually an older version) to work with a new version of iOS on your iPhone. As for which specific software is updated (system files and/or iTunes) I do not know, but this update will not update your Mac to a newer version of the operating system.

I saw this window pop up after I'd updated my iPhone 8 to the latest iOS some weeks ago. My iMac is still running Mojave because of some 32/64 bit app incompatibilities.