What makes a good fanfiction summary?
The answer can easily be found if one thinks about the function of a summary. It's purpose is to tempt the reader to read the whole fic. There has to be something that hooks the reader.
How does one create a hook for the summary?
The key elements are the main characters. They must be introduced in the summary. A fanfiction reader most likely is interested only in certain characters of the original work. If the summary fails to mention those characters, the reader skips the fic. If the writer knows her readers, she knows in which characters they are interested. Reviewers are valuable sources of information. In case the writer doesn't know the reader base of her stories, she needs to picture in her mind a typical reader. The writer knows best herself: to write to the people like herself could be a good choice.
The second ingredient that is needed for a good summary hook is the setting of the fic. Setting can be found within the original work or it may be created for the story, but the reader wants to know where the story takes her. For example, a fantasy setting might be the right setting for one reader but a turn off for another. Three things should be told about the setting: time, location and everything in which the fic takes place. However, for the summary in fanfiction archives the main type of the setting is often enough. The setting initiates the main background and mood for the story.
The main types of setting:
alternate history, campaign setting, constructed world, dystopia, fantasy world, fictional city, fictional country, fictional crossover, fictional location, fictional universe, future history, imaginary world, mythical place, other worlds (science fiction), parallel universe, planets (science fiction), simulated reality, virtual reality, utopia
The third ingredient that is essential for a good summary hook is
the main theme. The reader wants to know what the main characters are up to. She also wants to read something interesting. To her, the theme must be a novel, unexpected, original, clever, and enjoyable idea. In this regard, readers differ from each other. For example, I've read thousands of fantasy books written by published authors. It's impossible to tempt me with any basic theme of fantasy genre, but for a reader that is just getting into the genre the basic themes would be novel ideas.
If the theme of a fic is a basic theme of any genre, the easiest trick to make it tempting for the more experienced readers is to include a twist to the theme. For example, one of the basic themes in romance genre is a mousy girl turns into a swan to get the prince. How to twist that? How 'bout the prince turns into a mousy boy to get the swan? Or maybe the girl turns the swan into a mouse to get the prince. Or the swan turns into a mousy girl to get rid of the prince.
Anything beyond the hook is unnecessary in a fanfiction summary that is written for an archive.