How to use Wireless Beaming
The first step is to install iPhoto on two iOS devices such as an iPhone and an iPad on which iPhoto is compatible. You then start up iPhoto on both devices and head to the "gear" icon which is the settings menu. You want "Wireless Beaming" set to On for both devices inside of here. As far as I can tell, you actually need to have both devices on the same wifi network for this to work, so if necessary turn on wifi and connect to a shared network. From this point, all you have to do is find an image and click the share button(pointy arrow) which brings up the share menu. Inside of that you will find an option for "Beam" that looks like a wifi network icon. Once you hit the beam icon you can then select up to 100 images to share, and you are provided with a list of devices to share the images with. Once you select the "Beam Photos" button, the receiving device will be asked for a confirmation, and within seconds the images are sent.
What exactly is Wireless Beaming
Wireless beaming requires both devices to be on the same wifi network. The Bonjour networking from Apple is working behind the scenes to create a zeroconf network that keeps it dead simple for the user. According to this article iPhoto Beaming: Under the hood - iPhoto Beaming uses a UDP service called _mobileiphoto._udp. The article also describes that it looks as though this communication is setup specifically for iPhoto only, and not as an iOS wide implementation of file sharing. To send the files, the source iPhoto looks for potential recipients, connects to them, negotiates a handshake, asks for permission from the receiver, and sends the files. More detail with flows can be found at the link above.
As ughoavgfhw pointed out in the comments, the Apple iPhoto site notes that the functionality works over wifi OR bluetooth, but I have not been able to verify this, and other users have noted it requires the same wifi network. I will be testing this on my own shortly.