Think of GitHub as Google Drive for code, with one superpower: it remembers every version of everything. A project's code lives in a repository (a "repo"), and every change ever made to it is recorded, along with who made it and why. Nothing is ever really lost, and any earlier version can be brought back.
That version history comes from an underlying system called git, which is why the platform is called GitHub: it is the hub where git projects live.
Why you keep hearing it
Because GitHub sits in the middle of how software gets built, including software built by AI. AI coding tools connect to GitHub to read a project and propose changes (see PR). Hosting services like Vercel watch a GitHub repo and update the live website automatically whenever the code changes. And when someone says a tool "is on GitHub", they usually mean the code is public and free to inspect or use.
What it means for you
If you build anything with AI tools, even a simple website, you will probably end up with a GitHub account and a repo, because that is where your project's code lives and how it gets to the internet. You do not need to understand git to benefit from it. You mostly need to know that the full history of your project is safe there.