Apple's next big product: a cable box
Apple's cable box:
Apple's upcoming TV device will probably be an enhanced cable converter box that people will be able to buy when they sign up for cable/internet service. Basically, Apple is going to sell a "smart" cable box the same way companies sell smartphones. People will also be able to buy it from Apple and other stores, and sign up for cable/internet service at the same time. People who only want internet service will be able to buy them also, as will current cable/internet subscribers.
When Steve Jobs said he "cracked" the TV problem, he was referring to how to sell set-top boxes and reduce the complexity. Selling the device when people sign up for service will be a lot more effective than trying to get people to buy a separate device, like Apple TV, afterwards. It also means people will only need one box for all their content.
The device will be like Apple TV but with a cable tuner built in. It will run iOS and have app support (including games,) cloud DVR, and cost less than $200.
Other companies, like Google, will probably offer their own cable box also (Android TV?) When people sign up for cable/internet service they'll select which box they want, Apple's, Google's, or the generic cable box.
Why it won't be an actual TV:
Steve Jobs didn't like TVs because of their low margins and low replacement rate. A cable box will have a decent margin and will be upgraded fairly often.
Why it won't be a new Apple TV with iOS and apps:
It would still have the same problems the current set-top boxes have. Most people don't understand why they would want another box hooked up to their TV. They just want one box.
History is repeating:
Apple revolutionized the music player industry with the iPod, the smartphone industry with the iPhone, the tablet industry with the iPad, and now they're about to do the same with set-top boxes.
Apple's going to sell a cable box running iOS that people can buy from cable providers that will be similar to Comcast's cable boxes that support their X1/X2 platform.
Like this, but nicer looking and with much better software: