(Hi!) I was struggling over on Lyrics.wikia with all the MediaWiki markup in their page skeletons when all you really want is to enter some data {{band: "Corduroy", album: "Out of Here", song:"Mini"}} and have a song template produce the markup. It seems like TemplateData could really help, so I came here to remind myself about it. Alas the extension page lacks a simple explanation of how TemplateData interacts with actual templates, nor does nor does it give examples of it in use. The page says "This information is available as a nicely-formatted table for end-users", but my recollection is the stuff you put in the template data is somehow made available to other templates for them to output in their chosen wiki markup. There's a conceptual piece missing (or a screw loose in the reader...).
Topic on Extension talk:TemplateData
TemplateData doesn't affect how the template behaves. It only tells VisualEditor which boxes to show when you insert a template.