When someone surfs to your website - they are looking to solve a problem. If they think you can offer a solution to the problem they have (anxiety, depression, relationship troubles), you have a shot at them contacting you and becoming a client.
First there are a trio of hurdles you have to jump. Hurdle #1 is the question "Are you credible and legitimate?" The quality of your website, the way you speak about what you do, the education and experience you describe in your bio will speak to this. Your photo will also resonate this. Credible and legitimate means different things to different people, and also would "feel" different in various helping professions. Think of what your ideal client would want to know to feel like you were qualified.
Hurdle #2 is "Can you solve my particular problem?" You might be a good therapist, but I've got an anger problem. Do you mention anger on your site? Is it listed in the issues you deal with? (Or, to weed out people, have you listed it in issues you refer out to other professionals?)
Hurdle #3 is "Do I resonate with you?" When I've asked clients why they chose me via my website, some point at the photo, some at being a New Yorker, some at my technology background. Most are looking for a male. I find people are looking for some tie, some common ground, or for the thing they need (an older therapist for more of a parental need, for instance). They want to like you, and they want to think you will like them and accept them and understand their lives. They want to feel comfortable with you. This may have some similarity to an "Imago match" that Harville Hendrix describes. To me, this points to including some information about yourself in your website. This may go against the psychoanalytic tradition of leaving all things clean & open to transference and projection, but I don't believe small details about our lives define who we are as practitioners or people all that much.
So when you design and write your website, imagine your ideal client, and keep those three hurdles in mind. Be truthful about who you are and what you do and who you want to attract and you will be rewarded with clients that match that intention!
Best! Peter