An Artist's Website is a website that, much like an Artist's Book, is itself a work of art.
Artist's Websites favor artistic intuition over design conventions. While most websites center their design around usability, an Artist's Website will often make design choices based first on expression, even (often) at the expense of usability. They can do this because they are made for a very specific audience: the interested and curious.
In spite of their eccentricity, many design elements on Artists' Websites turn out to be intuitive and useful, in addition to being expressive. Think of them as experiments in web design, and they can be a source of ideas for anyone interested in design, interaction, and information on the internet.
I haven’t seen it very often, but a regular blog site is a great way for a prolific artist to display his or her work.