Microsoft Publisher is installed as a part of the free Office 365 suite of applications Maranatha Christian Academy offers to faculty/staff and student in our school. It is not like the other Microsoft tools that have online components or apps. As such it really only "exists" on the machine it is installed on. Users should still find a degree of integration with OneDrive storage, etc. but it is not as intuitive as the other tools.
That doesn't mean don't install it or avoid using it, just remember you will need to save it separately to your computer and/or sync it with your OneDrive for Business tool on your machine. Whenever possible, to make it easier for the user, we encourage the use of Word 2016 which includes many templates that create many of the same things most users will need instead of Publisher.
There is no Microsoft Publisher for Mac.