When I first switched on an Apple Macintosh computer in 1987, the first thing I saw was a tiny icon of a computer smiling at me. The "Happy Mac" eventually disapeared fifteen years later, but I still see it as an (if you excuse the pun) iconic example of Steve Jobs' philosophy of what computing was supposed to be about.
You could instantly see that Jobs was always emotionally involved in what Apple was doing. His keynotes weren't your average business presentations, they were events that everybody looked forward to. When he introduced a new product that he was excited about, like the iPhone, his eyes sparkled, and his enthusiasm translated to everybody in the room. Even when miscommunication happened (as during the early stages of the iPhone 4 release), it seemed to be because he was so emotionally connected to his products.
Jobs didn't just market products emotionally, he had them designed so that they would appeal to users in an emotional way. From the Happy Mac to the first bondi-blue iMac, to the first version of OS X that looked "so delicious you want to lick it". It's probably why the products create such strong emotional responses and why discussions between Apple users and Apple haters tend to heat up to ridiculous proportions.
Under Jobs' guidance, the company placed priority on preventing anything that could disrupt the emotional interaction between user and computer; this is the main reason why Apple's interface guidelines and the restrictions the company places on developers are so strict it's legendary. Still, the result speaks for itself: if people talk about hitting a computer or throwing it out the window, they never talk about an Apple Mac.
More important, however, and what really distinguished Jobs from just about every other CEO in the business was his ability to think outside the box. In the course of his career, he constantly questioned every established wisdom of the business. In sharp contrast to the "embrace and expand" strategy employed by Microsoft and many other companies, Jobs was never hesitant to tear things down and rebuild them from scratch, constantly looking and going in new directions rather than adding layer upon layer of basically the same thing.
Unlike other CEOs, Jobs saw interconnections and interdependencies that reached far outside his company into the world of his users, and he was ready to shift the paradigms when he deemed it necessary. Computers are all about technological specifications? Let's concentrate on the user interface instead. Customers want an extensive choice of products? No, a handful is more than enough. Video editing is for professionals only? Welcome iMovie. Apple is a computer manufacturer? Let's revolutionize the mobile phone market.
It was Jobs' way of thinking, his realization that a company's business does not end at the walls of its buildings but that it is a constant interaction with just about everybody, that transformed Apple from the ailing computer manufacturer of 1997, almost ruined by single-minded business executives, into the cutting-edge company that it is today.
Steve's energy and his unique vision will be sorely missed.