The Air moniker is due to the weight reduction, which is substantial, trimming off nearly half a pound from the iPad. The weight reduction is due to the change in dimensions of the iPad, the frame around the iPad has been narrowed, and the batteries are now lighter. The processor has been upgraded to an 1.4 Ghz Dual-core A7 (up from A6X in the 4th gen, and ARM Cortex A9 in the 3rd and 2nd generation iPads), which results in a very snappy response time. The improvements to the processor should help with a lot of those 3D apps. Additionally, the Air now has a M7 motion co-processor.
Setting up the iPad Air was extremely quick, and once I connected it up to iTunes, there was an option to restore the iPad from a previous backup (in this case, my 3rd Gen Retina iPad). Using the backup, reduced the amount of available capacity substantially, and within a few hours, I found myself out of drive space. My guess is that using the backup, it copied over all the application data, without checking if the application was still in the library. In my case, I had several apps from an old iPad that were no longer in the App store. Additionally, the new apps included with the iPad are pretty substantial in size, totalling about 3GB in total.
I cleared the data and reset the iPad Air to factory state, and reinstalled the Apps one by one -- while this worked for my iPad Air, users which have more data on their iPad may want to consider making sure they have their app data backed up before reseting after a restore. I'd also suggest that 16GB (12.8GB) may be too small for most power users, and that they would benefit from one of the larger capacity iPad Airs.
Battery life still seems to be very good with Apple advertising 10 hours, which is for WiFi/Surfing/Video and Music. Some reviewers have reported 12 hours or more.
Apple includes a 12W USB Lightning charger.
I did find that even though I had no trouble charging the iPhone 5 through a Lightning cable connected to USB hub, using that setup did not charge the iPad Air.
The new iPad Air is a good deal lighter than it's predecessor, and with all the improvements, there's only a few changes I'd like to see in the upcoming models -- the inclusion of the fingerprint sensor found in the iPhone 5S, and a bigger base capacity.
It's definitely a evolutionary change, and while I suspect it won't change the landscape of tablets or apps much, I think I will enjoy the new faster, lighter iPad quite a bit until the next revision.