iTunes wireless syncing allows you to interact with your iPhone (or iPad/iTouch) in iTunes without having the deviced plugged into your computer via USB cable. This can be nice if you don't have the cable handy for a quick sync of a few songs and photos, or if the device isn't at your computer. I frequently take care of backups for my iPod Touch this way, since the iPod Touch sits on the other side of the house acting as a baby monitor most of the time.
With wireless syncing, you can sync your iTunes library (copy music files, tv shows, photos from your photo library, etc of usual iTunes sync,) make backups, and do a bit of iTunes configuration — all without the device plugged into the computer, as long as the device is on the same wireless network as the computer running iTunes.
How to setup wireless syncing in iTunes:
Plug your device into your computer, and open iTunes. (Yes, you do need to plug it in once!)
Select your device in iTunes. Your devices will either appear as a button in the upper right, or in the listing along the left-hand column, as pictured here:
Click on the device on which you want to turn-on wireless sync, and scroll down to the "Options" section of the "Summary" tab.
Check the checkbox "Sync with this iPhone over Wifi." Note that it will likely say "iPad" or "iPod Touch" if that is the device you're using :)
That's it! Since iOS6 and iTunes 11, wireless syncing has been a lot more stable than it used to be, but definitely still let us know if you have questions or issues in the comments section below. If you have the device and a cable handy, you should still plug-in if you plan to transfer a lot of data (like syncing a whole new set of albums, or backing up a phone for the first time ever) so that the file transfer goes much more quickly.