Basically it patches bugs found in the original game and provides new engine features. RA2YR engine is not like modern game engines, you don't have a scripting language, everything is configured via config files without the need to code, hence modders can't implement custom game mechanics apart from what the engine provides. For example, per-unit shields with additional HP and different armor were not possible to do, with Phobos it is possible.

Scroll through the extension docs:

https://phobos.readthedocs.io/en/latest/New-or-Enhanced-Logi...

They have recordings of most of the different features Phobos enables.

Hopefully there will be in future. But for now the docs do have fancy GIF illustrations of Phobos features used, which is the closest you can get.