Many people complain that AT&T is the reason they either won’t get an iPhone or that iPhone service is bad. So, why is the iPhone exclusively on AT&T?
When Apple was creating the iPhone the company realized that it would need a partner that would be able to deal with a completely new product. The sales model would be different, the phone would cost more, and the users of the phone would tax the nascent data side of cell communications. Apple couldn't just drop the iPhone on any and all carriers, because at the time of release and as things have continued the iPhone pushes the boundaries of what's currently available and what will be available. Apple could not risk that the iPhone would be with a carrier that wouldn't or couldn't keep up with the evolving uses Apple hoped for the product.
AT&T was willing to essentially refocus their company to match Apple's vision of the future of cell phones and persistent and pervasive data access. AT&T believed that working with Apple would completely change their company and the market they served. They were right, clearly.
None of us know the specifics of the deal that was made, but we can safely assume that AT&T had to commit to a large scale and ongoing restructuring of their network infrastructure in exchange for exclusivity and that likely this continues to be the case. In other words, AT&T's cell business is now largely based on iPhone and iPad usage and recognizing that keeps them motivated to answer Apple's ongoing needs. Apple has a partner that is strongly motivated to please and actively engaged in continued improvements at all levels. There's no way that AT&T thought up the idea of a month-to-moth data plan for the iPad!
For the other side of things, Apple knew they needed a carrier who would be responsive to a market that was literally changing the way the network was being used. Additionally, as the market changed and adopted the iPhone model Apple knew that continued success would require that the carrier be willing to bend to the changing conditions.
Much as we like to whip AT&T for its failings, the truth is that while Verizon was capable of modifying their network as need demanded and they could have adjusted their focus to match what Apple wanted, Verizon made it very clear to Apple that Verizon would not bend over backwards to accommodate this new device. Even today, while Verizon publicly say they would welcome the iPhone they are not willing to do what is required to ensure that the iPhone user will get a consistent experience.