A Claude Artifact is a piece of content Claude generates in its own preview pane, code, a document, a small interactive app, that renders next to the conversation instead of only appearing as text. It is genuinely useful for checking work in progress, and it is not, on its own, a public website: the preview lives inside your Claude session, visible to you and whoever you explicitly share it with there.
Turning a finished artifact into something anyone can open at a normal address is a separate step.
For how artifacts differ from a real website and what it takes to publish one, see what are Claude Artifacts, create, edit, and share them.