Servers are assigned one or more badges that they conform to. Some badges may redirect to external links that the servers own and generally refer to, e.g., a homepage or official repository. A badge doesn't necessarily mean that the server is better than the others; it is to represent a server's validity, activity, and wiki. Badges selected for a server doesn't relate to Discord's own set of badges.
The server is owned or moderated by an established and registered organization, a company, project members with sufficient headcount. The Home badge points to its identity.
The server is owned and moderated by moderators of a preexisting Reddit forum, though not all subreddit moderators may be involved. The server is officially recognized as an associate community by the subreddit.
Official website of the server, it's a clickable badge. The webpage may contain helpful information about the server, knowledgebase, donation information, social media links, et cetera.
The server has an open git repository, may contain useful resources, Discord bot source code, and other developments. This clickable badge redirects to the hosted repository e.g., GitHub, Gitlab.
Some servers contain these tags. Tags are nothing but a reference to something generic to save content space.
A community with a wide range of topics, each of them is equally productive in activities. It has so many active channels that it's impossible to squeeze in all of them in Notable channels.