For me its mainly:

  - the ability to update every page on my site at-once in a uniform fashion (want to change the page layout or add a link in the footer, either you're manually editing a hundred HTML files or a couple lines in a single template file)

  - Syntax highlighting. My blog has code blocks so I would have to manually invoke a syntax highlighter for each code block (and every time I update the code I'd have to do it again).

  - auto-invoking graphviz and gnuplot. Similar to the code blocks, I write graphviz dot and graphviz blocks as code in my blog posts and have my static site generator render them to images. If I was manually writing the HTML then I'd either end up committing the built binaries (rendered images) to git (which, of course, is bad practice but ultimately inconsequential when talking about small SVGs for the few charts/graphs on my blog) or I'd have to have a "build" step where a script invokes graphviz/gnuplot to output the images which is the first step on the road to a static site generator.

  - Avoiding name collisions with internal anchor links (the kind with the `#` symbol that scrolls the page). I use these for footnotes and code block references. I could manually assign names for these for each blog post, but when combining multiple blog posts into a single list-view for the home page, there is the risk that I might reuse the same `#fn1` anchor across multiple blog posts. Using a static site generator, I don't need to concern myself with naming them at all and I have my static site generator assign unique names so there are no conflicts.