When someone changes something in the "authoring" instance of the application the change initially won't have any effect on the public instance. In order to take effect on the public "subscriber" instance(s), the change needs to be "activated" - in a properly configured Magnolia setup this then pushes the changes to the public instance.
Virtually every type of node can be activated and pushed to subscriber servers - not just web pages, this is important. When you look at the administration console of the authoring app you'll see a lot of little red lights next to everything, a red light indicates that that particular node is not published, a green light indicates that it has been published (but see below for caveats), and a yellow light indicates that you've changed something since it was last activated and you'll need to activate it again to push the changes to the public server.
In the Config/subscribers/subscriberConfig section of the authoring app you can set up details of what machines to activate changes to. You'll normally be pushing activated nodes to the public instance, but one can list several machines in this list for mirroring purposes, or other arcane setups.
Editing the node is reasonably self explanatory - you point it at your public server. Please make sure that activation works after you have configured a new subscriber. Create a new page, activate it and see if it shows up where it should (i.e. at the subscribing instance). Watch the logs if it does not, they will tell you why activation fails. The GUI will make sure that you cannot activate unless an active subscriber is configured, but Magnolia doesn't double-check if activation has actually worked, and will show the node as published even if it might have failed.
One reason why activation can fail is that you lack the permission on the subscriber to actually write content where you wish to write it to. When you activate something in the authoring server it uses your username and password to log into the subscribing server to actually do the publishing. This means that unless there is a user on the subscribing machine (the public server) with your username and password and privileges then the activation process will fail silently.
Since users and roles are nodes just like any other they can be "activated" too. If you create a new user on the authoring instance, remember to "activate" that user so that the users details will be pushed to the subscriber server(s). One thing I really need to stress again, because it was very counterintuitive for me, is that there appears to be NO synchronisation process between the servers - the authoring server merely pushes changes on demand to the subscribing server. This seems to make things extremely brittle - if the authoring server and the public server get out of sync for some reason it's very hard to tell what gone wrong and very hard to fix it. The worst case of this appears to be if you change a users' password and forget to "activate" the change - that user will then be unable to make any changes to the subscriber server. If the user in question is the superuser very awkward things can result.
Like any system, Magnolia has a number of concepts you should be aware of before you get started with installations.