They provide a nice dashboard for creating Mongo collections (which they call Classes).
You write "cloud code" in JavaScript. You can write beforeSave and afterSave functions which are triggered before/after you save a document. You can also write "cloud functions" which execute within parse-server and interact with the database.
The result of this is that you can perform a lot of heavy lifting and consistency logic in one place, "the cloud." That way you can build clients in multiple languages (like an iOS app, Android app, web app) that only need to worry about their platform specific details.
Their original value prop was for building mobile apps, but since the ecosystem is pretty mature with a client in every language, I find the benefits extend to writing multiple clients for any purpose.