You deploy these flows in their engine, where they're kept alive. You can self-host the engine, but they also offer it in their cloud.
Then you can choose to frontend it with a HTTP API that you build in their builder, and choose to put it in your organization's private store, or the public store for others to use. There's management dashboards too.
There's hundreds of other products or product combinations that could be described in the same sort of vague language, but MuleSoft ships and supports a particular environment and a particular collection of tools that does it pretty well.
Ultimately, the goal of all of these is the reduction of the effort around every other piece besides the parts that are custom to your unique circumstances.