Let's start from the bottom and work our way up. Jeff Atwood wrote a post about meta tags that was referenced in an older discussion about tagging here. It contains the following definition of meta tags, courtesy of Aaronut on meta.cooking:
Meta-tags are actually a subset of a larger problem that I usually call dependent tags. These are tags that don’t say anything by themselves – you can’t tell what the question is about unless they’re paired with some other tag (or several of them). These tags are a problem because people don’t realize this and will often use that as the question’s only tag.
Meta tags tend to cause two types of problems: they squeeze out tags that would otherwise be applied to the question (and thus need a second pass to be tagged properly), and they cause confusion as to what, exactly, they mean. From Jeff's post:
Best practices to whom? Beginner by what criteria?
Is such a tagged question for beginners at that game? What about people with experience in similar games, but none with that particular game? How much experience makes you more than just a beginner?
Why would someone follow the beginner tag? No one has enough experience with all games to be able to answer beginner questions on all games; neither would someone be interested in beginner's questions for all games. The tag itself is meaningful only in combination with other tags, but cannot be followed in combination with other tags. Yes, it may assist you with respect to searching ... but would a question for beginners not also contain the word "beginner" itself? Tags are not intended to be substitutes for searching – we already have that ability.
Number of followers is a useful metric for evaluating tags: ideally, we would look at something like views per followed tag vs. views per non-followed tag, but that's really not possible, because one advantage of following/ignoring is that you can scroll through questions without clicking and still get an idea of the ones you're more/less interested in. (That is, essentially, what I believe tags are designed to do; they also serve as a funnel for searching, so that people don't have to try five different spellings of a particular game to get all the questions for it.) Let's look at the first page of tags on the main site.
rules has 5 followers and 455 questions. That's generally an indicator of meta-ness, and of course rules isn't a game called "rules" (which, btw, is one reason to avoid meta tags on sites like these: it can cause confusion if we end up getting questions on such a game). Does that tag give you any indication as to whether or not you might be able to answer the question? No. It just suggests that the question is about rules ... as would most questions be on a site like this. (See also this discussion on RPG meta.)
magic-the-gathering has 99 followers and 391 questions. People follow it because they play MTG or are interested in it, presumably. A question tagged magic-the-gathering gives you an indication, through the tag alone, whether or not you might be able to answer it, and further, gives you a reason to follow or ignore it, something that rules does not.
strategy: 16 followers. house-rules: 4. game-design has 23, but that makes some sort of sense, because in another context the topic is deep enough to merit its own site. Of course, on that site, nothing is tagged game-development.
As far as what the actual purpose of tags is, on this site? I don't know that anything has changed since that original discussion. Here's an excerpt from Mag Roader's answer:
In my opinion, most questions should have 1 tag - the game they are asking about. I'm not seeing much value from the extra tags.
With that in mind, I would say the purpose is to link questions to the game or games about which they're asked, or to a topic like history if the question is not game-specific but is also on-topic for the site.