Design is a lot of things to a lot of people. To some, it's simply the way a product or website looks. For others, it takes a much more holistic meaning. For them, design encompasses everything about the product that is being designed, from the way it looks and feels to the way it is put together, to the way the end user will use it.
There are many schools of design that focus on various aspects of design as a whole. For starters, there is graphic design, which is perhaps the oldest kind of design. Graphic designers work towards making sure an item is aesthetically appealing instead of aesthetically appalling. They work with anything that is related to a project's visuals, from designing logos to figuring out the best way to arrange information.
User interface (UI) design and user experience (UX) design deal with how a product's design affects its user. Designers strive to make it so the user has easy access to all the features they need to use the product without spending a lot of time learning how to use the product. In other words, the goal is to make things as intuitive as possible. This includes choosing icons that elegantly convey functionality and producing products in a shape that is ergonomic and usable. UI and UX have a lot in common and rely on one another, along with the item's graphic design.
Design is a complex profession that asks a lot of a person while offering few hints towards what is best practice. In fact, popular advice for designers is to make their contribution to a project feel like a little while being a lot. This is difficult to quantify, but it's easy to identify when it arises. Think the design of the original iPod, with it's single button and round scroll wheel, or the difference between a text-based user interface and a graphical user interface on a Linux computer.