Forget everything you know about tags for a moment, because TiddlyWiki has a slightly different notion of tags from most tools.
TiddlyWiki tags are a way of relating two tiddlers. (You might consider a tag a special kind of link to another tiddler that's stored in a tags field instead of the text field.) Specifically, the type of relationship expressed by a tag is membership. If I create a tiddler about myself called Soren and tag it Person, I'm saying that the Soren tiddler is a conceptual member of another tiddler called Person; or, put another way, “Soren is a Person.” As with traditional links in TiddlyWiki, this is a bidirectional relationship and you can search based on that relationship in either direction: Person will know that it is tagging Soren, while Soren will know that it is tagged Person.
Making tagging into a means of relating tiddlers rather than a means of sticking little labels on things dramatically expands the range of things tags can be used for. Traditional tags can only be used for “tag-based” organization – you can filter your content based on its having or not having a particular tag or set of tags, and that's about it. You can still do this with TiddlyWiki tags, but you can also use them to create more complex structures like multi-level hierarchies – seemingly the antithesis of traditional tags. If tiddler C is tagged with B, and tiddler B is tagged with A, you have an A > B > C hierarchy. TiddlyWiki provides tools such as tables of contents for viewing these hierarchies.
In some way, this also just makes sense: if everything's a tiddler in TiddlyWiki, why should tags be any different?
Just like you can link to a tiddler that doesn't exist yet, you can tag a tiddler with a tiddler that doesn't exist yet. For the more traditional methods of using tags (e.g., filtering tiddlers based on whether they do or do not have a particular tag), you never need to create the tagging tiddler at all – but you always have the option if you need it, or if you want a convenient place to describe what the tag is used for.
If you look at the top of this section, you can see that its tiddler is tagged and . The colored ellipses around the tag names are called tag pills, and if you click on one you will see a list of all tiddlers with that tag. Usually the tagged tiddlers are shown in alphabetical order, but we'll learn later that they can be put in any order you like.