Siri is the name of Apple's virtual assistant with a personality straight out of Pixar. You ask Siri questions or ask Siri do to thing for you using your voice, just like you would ask a real assistant, and Siri will get to working helping you stay in touch, on time, and informed. There's even a related service called Dictation that lets you enter text almost everywhere with just your voice. Siri and Dictation are online services, so you need to be connected to the internet to use it.
Siri is still in beta, and is limited in the number of devices languages and locations it supports. Also, Siri is currently limited to the iPhone 4S, though Dictation also works on the new iPad and soon, the Mac with OS X Mountain Lion. Apple has announced, however, that Siri will be coming to the new iPad, along with several more languages, locations, and features with iOS 6.
We'll expand this guide to include all of that, and more, when it becomes available this fall. But here's what you can do right now: