It's all about the message. Early in a new project I like to come up with a short, simple – and memorable – tagline or catch phrase that encapsulates that message; such as what I have for this site: "How I make a website".
How often have you gone to a site and found yourself wondering what you are doing there? That should never happen. Visitors might leave because it isn't what they were looking for, but at least you should have your say.
I usually do, but nothing says you have to include your tagline on your site. Google doesn't, but they do have one: "Return highly relevant results for every query". Even if your tagline isn't going to be displayed, write one. A good tagline gives you and everyone involved a well defined and focused idea of what the site is about.
If your message is lucid, to the point and catches a visitor's interest, they will stay.