Code sitting on your computer is not a website yet. Something has to run that code on servers, give it an address, keep it fast and keep it online. That is hosting, and Vercel is one of the most popular hosting services for modern websites.
What made Vercel a favourite is how automatic it is. You connect it to your project on GitHub, and from then on, every time the code changes, Vercel rebuilds the site and puts the new version live, usually in about a minute. No servers to manage, no upload buttons. The free tier is generous enough that many personal sites never pay anything.
Why you keep hearing it
Because Vercel sits right in the AI-builds-websites boom. When someone builds a site with an AI coding tool and says "and then I deployed it", Vercel is very often the place they deployed to. The company also makes v0, an AI tool that generates web pages from a text prompt, which keeps its name in every "I built this with AI" story.
What it means for you
"Deployed on Vercel" just means "this is where the site lives online." If you ever build something with AI tools, you will meet Vercel or one of its competitors at the final step: the moment your project stops being files on a laptop and becomes a real address on the internet.