Be sure that the git tool is installed on your Mac computer (see part 3). You also must have an internet connection to get the files from the update server.
Now the only thing you need to do is to doubleclick on an icon inside your MAMP folder. That's all .... really .... it's easy!!
Please look for the script UpdateMoodle.sh. If you doubleclick this icon then the system utility Terminal opens and the update process starts automatically. You must allow to connect to the Moodle internet server ... but think about this fact only if a system tool asks you.

The git tool connects to the Moodle internet server and looks for all those files that must be downloaded. In its first run the update script needs to download the complete Moodle package in a special git format. In all next runs the update script will only load the changes. The update needs a few moments to find all updated or new files but then only those files are transfered. Please wait for some seconds until it's done.
The files are downloaded into a temporary folder. You can see the process in the terminal window.
If the update takes too long you may break with <strg>-C. It doesn't matter because only text files are copied. On break the process stops working. If you restart the update the git tool will find those files that need to be renewed again.