Just a few suggestions based on other SE sites, how they handle this, and what I've found. I've gone to some of the larger ones to see how they do it, and some smaller ones to get a more rounded view. I'm mostly looking at the excerpts, because that's what most people see, though the summary shouldn't be discounted of course.
Arqade has a lot of tags, and seem to have tried tag standardization in the past. Looking at the most popular tags shows that there is some consistency, though it is not complete. Some of the general structures seem to be something like the following...
[Company]'s [genre] game [short blurb]. This tag is for [...]
A [genre] [year of release] by [company]. [Short blurb].
[tag name] is a [what it is].
This tag should only be used for questions about [...]
See: Xbox 360
[tag name] is for questions regarding [...]
See: Technical Issues
Chemistry is also in beta, so it may be a good place to look for ideas. Their top tags are structured generally as follows...
[tag name] is a [branch/field] of chemistry that [...]
See: Organic Chemistry
In [a field of chemistry], [tag name] is [...]
See: Crystal Structure
This tag should be applied to [...]
Questions relating to [what the tag is].
[Simple textbook definition].
As seen on their tags page, it seems a lot of the most common tags on Electrical Engineering have the following structures...
[tag name] is [definition].
The majority of SO's most popular tags are very similar...
[tag name] is [definition]
See: Most of them.
Even some of their newer tags have similar structures.
Writers is also in beta, not many more tags than Chemistry (both have slightly more than Worldbuilding). Writers has the following that I can see...
[tag name] is [definition]
Some tags are a bit shorter.
I like two of the above myself as they both strike me as interesting and informative, as far as tags can be at least. Looking at Writers[characters] and something on SO (I'll use Java since I can't figure out how to link C# properly), I like what I see.
The Characters tag is witty in a way, yet still feels professional. It's short, concise, and gets its point across while also being a bit funny.
The Java tag looks well written to me, with a very specific definition of what it is that (I don't know much about Java) prompts me to want to look into it to read more. Behind that, there is so much information that I immediately know where I'm going if I want to learn. That last part may not be what this site will do, but it's a nice feature.
I really like the format of the Java tag, but writing it purely that way may not be a good fit for a site where we may want to guide the writer with the tag. Look at biology and you will see what I mean. It references some special requests about biology questions in that it asks for special parameters to be defined, if necessary, in the question. That can also be a good target for the main body of the tag: put good example questions in there. If people get stuck in how they should cover everything, they can check that out.
I might write it as follows:
Biology is the science of life and living organisms.
Use this tag for [...]
Questions about biology should [...].