You should use that same logic in your web design. If people are attracted to your website's design, they will most likely be attracted to your business. It's pretty simple, really.
Here's what makes it difficult, though. What's good design changes pretty frequently. Let's take Amazon.com for example. It's a pretty widely used website that everyone is relatively familiar with it. Here it is:

Looks pretty clean, right? Easy to navigate, a couple of call-to-action boxes on the sides, lots of content to look at. All in all, this is a pretty solid site. No reason to change it, right?
WRONG!
You see, what I didn't tell you was that the pic you see to the right...is Amazon from October of 2009!! BUM-BUM-BUUUUUM! Sneaky, huh?
Let's take a look at it now:

Oh yeah, much better! You can kind of already tell what they did differently. On the left side, it looks like they took their already established categories and made the sub-categories branch off as you click through. In the 2009 version, the sub-categories are just listed. Listing is not really the best idea when it comes to design, unless you have a manageable amount of them. Too many can just dirty up the page. Agreed? Agreed.
If you want to get a good idea of how design changes over time, go to http://web.archive.org for a chronologically ordered archive of popular websites. You can see what they looked like in the past. It's pretty interesting if you ask me. *pushes up glasses, takes hit of inhaler*
If you want your mind really blown when it comes to website design, look no further than everyone's old favorite search engine, Yahoo!

This is Yahoo in 2009. It's obvious they were trying to capitalize on Google's simplicity and easy-to-use...ness. Then, Yahoo just kind of decided "Whatever. We're not Google. Let's do this!" and then put this out:

Quite a difference, no? They put that photo slideshow for all their News stories, so there's a visual element that makes it more appealing to the eye. They still have their many different Yahoo-related pages, but they're organized in a much cleaner, visually-appealing way than before.
In conclusion, web design is important. Now, here's a picture of a chimpanzee riding a pony!

