One easy way for developers to bring non-gamers into the gaming world is to make a game easy to understand and control. Console-makers have a hand in this as well (pun definitely intended) when they design their control pads. There are a few important aspects that a controller needs to have in order to make it good, and the PS4's Dualshock 4 definitely does the job well.
First and foremost, the control pad needs to be comfortable to hold. I have rather large hands, and my girlfriend has very small ones, yet we both find the controller somehow very easy to grip. It's natural and comfortable- we can both reach all the buttons without straining, and long gaming sessions never cause our hands to cramp. In addition to being the perfect size, the Dualshock 4 is also very lightweight, which certainly adds to the comfort factor. The Dualshock 3 was definitely inferior to the Xbox 360 controller in the comfort aspect- most people complained about the trigger buttons, which could be slippery. The Dualshock 4 fixes this with triggers that your fingers will stick to, making it easy to play racing or shooting games.
Starting with last-gen consoles, wireless controllers were the norm. The Dualshock 4 continues the tradition with an 8-10 hour battery life, which is arguably actually pretty small for a controller and a definite step down from the Dualshock 3. This is admittedly a big negative to the controller, but it's the only negative, and I've found that remembering to charge the controller in between gaming sessions leaves me with enough battery power to game unimpeded for as long as I like. This, of course, takes points away from the convenience of the control pad, and can be pretty annoying for a house with more than two gamers (the PS4 only has two charging ports), but for most people the low battery life is nothing more than a slight inconvenience - and becomes irrelevant when having two controllers, as they allow you to cycle between either when using a simple accessory like the PowerA DualShock 4 Controller Charging Station, meaning battery will never be an issue.
The Dualshock 4 features stunningly accurate motion sensors, a touch pad, and a "share" button that allows gamers to upload screenshots and clips to the Internet on the whim.
One of the coolest unique features that I like about the controller is using the motion sensor for typing. Instead of using the D-pad to select letters on an on-screen keyboard, you can move the controller itself to sweep the cursor across the keyboard and type quickly and accurately. One of my favorite games right now, "Rocket League," features text chat, and it's so easy to send messages during the game without taking up too much time.
The "share" button is really cool too, especially during the age of social media. It's incredibly easy to upload clips of clutch victories and post screenshots of scoreboards or funny glitches, allowing you to share your gaming experiences with the world without having to spend time and money on getting screen-cap devices, etc.
The touch pad hasn't really gotten a lot of use in AAA games yet and mostly just serves as an extra button. More buttons isn't really a bad thing, but I'd like to see this unique feature of the Dualshock 4 get some more love.
The Dualshock 4 isn't perfect, but it's a very good control pad that's comfortable, responsive, functional, and has a lot of really cool features. The inconvenience of the low battery life, which isn't an issue if you cycle between two, is definitely made up for by all of the upsides of the controller, making it a solid product that's fun and easy to play with - after all, there's nothing else around that comes close to the Dualshock 4.