Whatever stage of your writing career you are at a website can be of some use. Of course if you are an established writer then it will make it easier for your fans to follow you, to chart the progress of your next book, get information about personal appearances and even stay in touch. If you are newly published then it is a great way of building a following, of communicating with your fans, and building your fan base by making it a point of first contact for those new to your work. For those still looking for that first break, for an agent and publisher, then a website can be a valuable marketing tool.
In the minds of the majority a website still equals professionalism. Having a website can indicate how serious you are about writing as a career. Agents are looking for a long term investment, not someone who has written one book and expects to retire on the proceeds. Setting one up is incredibly easy and can be done in a couple of hours.
The website itself can go further to demonstrate how serious you are by being a better way of presenting yourself than a mere CV, sample chapters and synopsis. Every agent/publisher has their preferred way in which they like to see submissions presented and there is little you can do in the way of variation within that, but a website is your own preserve, you can present yourself in a far more arresting way. This does not mean flash over substance, it simply means taking control of how you present your work, how people meet you as an author. Rather than just listing whatever previous work you have done, short stories, articles, even blogs, you can have links to it, or just make it available on your site. Rather than just having a synopsis for your book, you can give it a page of its own, laid out how you please and illustrated if appropriate. You can talk about your inspiration and influences.
Having a website also gives you something immediate to show people. If you are networking, trying to raise some interest in your work, it is so much easier to give a new contact your website address than it is to get their postal address, find out how they like submissions to be presented, put together a package, and send it off. By the time you have done all that they may have forgotten they even met you. A website is tough to beat for immediacy.
None of these things are substitutes for content and remember that if the basic idea is not there in your initial submission then no agent is going to get as far as your website, but taking control of how those ideas are presented is just another way of getting an edge.