It gives Apple a share of the lucrative over 4-inch phone market. That's where Samsung et. all make their money and Apple currently makes precisely zero. Adding a big screen iPhone 6 not only gives Apple access to that premium customer base, it takes money away from their competitors.
It eliminates size alone as a differentiator. Since the North American market is subsidized, it's the equivalent to walking into Best Buy and seeing all TVs, from 50-to 120-inches, for $200 or less on-contract. Adding a big screen iPhone 6 forces the competition back to areas where Apple's strong, like experience and ecosystem.
It makes the iPhone more functional as a primary computing platform. Some people don't want to have to carry around — or simply can't afford — multiple devices. They need a phone, but they want something closer in size to a tablet. Adding a big screen iPhone 6 fills that gap.
It makes the iPhone more accessible. Whether it involves eyesight or motor skills, a larger screen can support larger interface elements, including type and images. Adding a big screen iPhone 6 makes the technology easier to use.
It allows software to become more sophisticated. One-handed-ease-of-use can be handled by gesture navigation and dynamic interface, but 1136x640 is a fixed constraint. Adding a big screen iPhone 6 opens the platform up for the future.
Apple says their goal is to solve problems and to make technology more mainstream. To make better products that improve their customer's lives. They don't just want to sell more iPhones — they're avoiding the high-volume, low margin market like the plague — they want to sell better iPhones to more people and increase the overall value of their ecosystem. That makes them more profitable, makes us happier, and ensures our mutually beneficial relationship lasts as long as possible.
That's why one size simply doesn't fit all. Apple has had at least two sizes of MacBook Air, MacBook Pro, iMac, iPod, and iPad on the market, and in most cases have for years. That allows them to hit the biggest addressable market possible with the smallest product lines possible. Phones are no different.
Just like 2011 when the iPhone finally hit Verizon, the problem a 5-inch iPhone solves is choice. Right now people have to choose between the iPhone and a big screen not-iPhone. With a 5-inch iPhone 6, we'll no longer have to choose.