Until now, the iPhone has had an exclusive on built-in texting via Apple's Messages app. That's changed in iOS 5, and now the iPad and iPod touch have joined the party. iMessage allows for free texting across all iOS devices running iOS 5 so long as they have internet access.
If you've already been using Messages on the iPhone or iChat on the Mac, you've already got a general idea of how iMessage works. It's a basic IM client with support for sending text, photos, videos, contacts, and locations to the other party. iMessage shows a small ellipsis when someone is typing a response, and at your option you can set up iMessage to send read receipts to the other party once you've read and received the message.
One of the nice features of iMessage is it allows you to set it up with the same email address on multiple devices. You can begin a conversation with someone on your iPhone while you're out and about, then pick up at exactly the same spot when you get home and use your iPad. Texting takes place virtually instantaneously; I had the above conversation with a TUAW staffer on the other side of the planet, and it was as seamless as you'd expect from a modern IM app.
On the iPhone, differentiating between texts sent via traditional SMS or through iMessage is easy. SMS texts you've sent will show up with a green background, while iMessage texts show up in blue. While you'll still have to pay the traditional fees for any SMS texts you send, it bears repeating that all iMessage texts go out over Wi-Fi or 3G and are completely free. I've also noticed that texts sent via iMessage tend to go out much faster than those sent via SMS. I don't know if that's a consequence of my wireless provider's somewhat lackluster network or whether there's something inherent to the SMS protocol that makes it slower, but the difference in speed is quite noticeable.
iMessage can send messages to any device that's running iOS 5. The iPhone remains the only iOS device capable of sending text messages to non-iOS devices, and the fact that there are still so many of those out there means iMessage isn't going to "kill" SMS texting any time soon. On the other hand, if everyone in your circle of friends has a device running iOS 5, iMessage could very well obviate the need for an unlimited texting plan on your iPhone.
Apple iPad Air 2
Apple iPhone 6s
Apple iPod touch 6th-gen