There are two areas we can look at when talking about simplicity: The product itself and the way it’s presented.
Often we hear about concepts like minimalism, reducing clutter, generous use of white space, and so forth. Those are design principles often applied to websites, UIs, and promotional materials. But unless you’re doing something like creating WordPress themes, those aren’t your products; they present your product.
Let’s consider craigslist. Yes, the craigslist UI is fairly minimalist, it’s relatively devoid of clutter (albeit in an anti-design sort of way), and there’s lots of acceptable use of white space.
But what makes that website work is the simplicity of the service: Post classifieds, read classifieds. Not a lot more to it than that. And so it works. The same design applied to a more complex product would not work nearly as well. In fact, I would argue that no design can make a complex product work as well as something as simple as craigslist.
I guess that’s why I find that in my development life, single-purpose stuff is so much nicer to use. A jQuery plugin that does one thing is often more memorable and useful to me than a utility library that tries to do too much (jQuery itself, of course, being an exception).
Now think in terms of visual design. You can showcase your product on a minimalist, clutter-free website, but if the product itself is too complex and has a steep learning curve, the design will likely have limited success.
There are certainly many exceptions. In addition to jQuery, CodeKit comes to mind. I wouldn’t necessarily say that’s a simple product, because it does so much. But it fills a huge need in the development industry, so it works well. Photoshop might fall into that category, too.
So again, I’m not minimizing the importance of applying design principles to our websites (or other media). But if the product the website presents is too convoluted and difficult to use, no amount of promotional material utilizing white space or minimalism will change that.
Thus, simplicity starts and ends with the product or service itself, not the way it’s presented.