There are three types of private add-ons that I know of:
1 - You have an unfinished mod that is not in a stable state to be released, which can lead to glitches or even crashes in the game, and you don't have the time or want to finish the project, so it's often abandoned.
2 - You have an add-on in the works that you're taking your time to develop so it can be released when it's ready, until then it can be considered private before it goes public.
3 - You have a fully functional mod that not only works perfectly in-game, it's also fully finished and ready to be publicly available, but you want to keep it for yourself and for a select group of players.