A Personal Package Archive (PPA) is a software repository for uploading source packages to be built and published as an APT repository. It is provided by Canonical (the company behind Ubuntu) and allows developers and enthusiasts to offer up-to-date versions of software to all Ubuntu users.
Use in MX Linux
Our policy is that we discourage installing Ubuntu packages on MX Linux as it can (and has) caused problems. However, MX Packagers can examine the components of the ppa to see if all their dependencies appear to be met, to look for anywhere Ubuntu and Debian have different names or locations for the libraries, and hunt for anything systemd related. So it would be prudent to ask them about particular repositories you are thinking of adding.
The open source video transcoder Handbrake releases nightly builds, and an interested user might want to get those through the standard package management system instead of downloading them one-by-one as they become available. A look at their Download page shows the PPA information, but also a link about technical information. There you will discover how to add the repository manually selecting an Ubuntu version that matches the Debian Stable base used by your MX Linux version (vivid is used for this example):
Now you can open Synaptic, click Settings > Repositories, and press the “New” button. Enter the information above, click OK, and reload. You will probably get a Apt GPG error, so just launch MX Check Apt GPG to find and install the key.