Source: http://gizmodo.com/5944578/what-is-miracast
Miracast is a lot like AirPlay...
AirPlay is a wireless standard that allows two devices to connect to each other to share movies, music, or other media. Miracast is the same thing, just not owned by Apple. Miracast is built on Wi-Fi Direct, which is basically just an ad hoc Wi-Fi standard. It lets two devices that have Wi-Fi in them talk to each other without having to go through your internet network. And unlike AirPlay, it will work with disparate brands and platforms. So ideally, your Samsung phone would be able to talk to your LG TV. Pretty great.
...but technologically better than previous attempts...
Unlike some of the older implementations of Wi-Fi streaming, like Intel's first stab at WiDi, Miracast will allow you to stream in full 1080p. You'll also be able to use media like DVDs and other stuff that has DRM on it, which had been a non-starter in the past. Miracast also does a bunch of nerdy grunt work behind the scenes; you should never have to worry about format or codec or anything else when streaming something—just click a button and play.
...that's got support from major chipmakers...
Qualcomm, Nvidia, and TI are all planning to support the standard, meaning your Tegra 3 phone will actually work with it. Hopefully, that means you won't have to pick and choose which phone or tablet to upgrade to if you want to keep using your Miracast stuff.
...and will be (or is) in a bunch of popular gadgets...
Samsung has been using a form of Miracast called AllShare Cast for a while now. It's built on Miracast, but it being on board with the certification means that stuff like the Galaxy S III or Samsung's beautiful Echo P TVs will fold into the rest of the tech world, instead of being sequestered in a sad little Samsung corner.
hopefully pretty soon.
The Wi-Fi Alliance announced the certification process for Miracast today, and announced that the Galaxy S III, the new LG Optimus G, and Samsung's Echo P TVs are all already certified. Others are being tested to ensure certification as soon as the holidays, and by early next year, hopefully we'll have a real AirPlay alternative for everyone not wrapped up in Apple's ecosystem.