The benefits of such a setup are numerous, especially for small sites and side projects:

Hosting a static website is much easier than a “real” server - there’s many free and reliable options (like GitHub, GitLab Pages, Netlify, etc), and it scales to basically infinity without any effort.

The how is also super interesting:

So how do you use a database on a static file hoster? Firstly, SQLite (written in C) is compiled to WebAssembly. SQLite can be compiled with emscripten without any modifications, and the sql.js library is a thin JS wrapper around the wasm code.

There’s more to the story, and the resulting solution is also open source.