Wrapping my head around what Publishing means in simple english with an example

"Publish to a server" means you upload your published content to some web server. For example, I have a web hosting package with a service provider, which allows me to upload my published Storyline content and then share the URL with clients. Here is one example. A "server" could also be a cloud-based storage solutions, like GoogleCloud or Amazon Web Services (AWS). Here is some info on cloud-based storage. These options work fine for content you want to make available "to the world". If you want/need to track learners' progress and/ore quiz results, your content needs to be hosted in a Learning Management System (LMS). There are lots of LMS options. For example, my hosting package also includes Moodle, a (almost) free LMS. It all depends how you want to make your content available.