It's simple: a generator that yields static pages to form a static site.
Static sites are the OG of the World Wide Web. When Tim Berners-Lee created the first web browser back before my generation was born (always late to the party), it was more or less simply a document navigator. Documents were just files in a hierarchical file system and hyperlinks led you from one document to another- just like navigating a Unix-like file system. Each document's content was stored the same way it was rendered. If you are familiar with the Web nowadays, it's obvious that it doesn't work like this anymore, due to the demand for dynamic content and the need for efficient storage.
However, some things don't need to be dynamic. Take for example this blog: there's no need for my content to be rendered dynamically. Most of the content won't change very often, and the content that does change will just be new pages. I might eventually run out of disk space for my files, but then I'll just migrate the site to a VPS. No matter what, generating the HTML for the page can happen way before a user tries to access it, in my scenario. It just makes the most sense to keep it simple (,stupid).
So what is a static site generator? At the most basic level, it's a tool that takes content in the form of files (typically) and generates a file system-like structure of HTML files. However, static site generators can do much more than that: templates can be applied, metadata can be gathered, images can be compressed, etc. Rendering content statically is generally much faster than rendering dynamically, and actually less vulnerable to exploits.
Check out Part 2 to find out how to choose a static site generator.