The Economist retains 4 lessons from apple:

1. Innovation can come from outside. In the case of Apple, the GUI (graphical user interface) was invented at the Xerox Park by a group that included Larry Tesler who later went to Apple to work on the Apple Lisa and the Mac. The Ipod OS (operating system) was designed by Pixo, an external firm. To do so, making a network of innovators, university and start-up is important.
2. Design around the user’s needs and simplicity, not the demand. You sell with demand but design by focusing on the user’s needs. When Ipod was launched there was no demand but Steve Jobs stuck to his instinct. In fact Apple as always integrated technology and simplicity with users in mind. Macintosh, Ipod and now the Iphone are all great innovations, but they were not the first. The characteristics of those innovations are not the novelty in functionality but the simplicity and user experience. It gives access of these novelties to a wider audience.
3. Ignore what the market says today and target new customers. The Ipod is an example. The simplicity makes the Ipod accessible to a wider audience. This innovation created the demand and consequently the market. Steve Job stuck to his instincts
4. Fail wisely. Most of the Apple success came from previous failures. The Mac emerged from the Apple Lisa failure, The Iphone is a response to the original music phone project with Motorola. When failure arises, learn form it.

In my view, the most important aspect is the Apple culture. It is not an engineering driven company but a design driven company. Decisions are not based on technical constraint. Of course, designers listen to engineers but they will sometimes ask them to go back to the drawing board and think again and be creative to achieve the design goal. For example Bill Atckison wanted the screen of the original Apple Lisa to be white instead of the traditional black in order to imitate the paper. Engineers at the time were strongly opposed saying it would consume more memory etc…but Bill stuck to his point and the engineers found innovative ways to achieve Bill’s design goal.

By being firmly centered on design and the user, more often than not, engineers will find a way to make the impossible possible. That culture is what in my view makes Apple stand out.