Here's some picture's from their demo gallery, so you can see and try it yourself. So tick different places in image to focus on that level:
By Lytro / Richard Koci Hernandez
Sophie Hernandez, 13, lost in her favorite book.
By Lytro / Jason Bradley
Shore entry in Monterey Bay, California
By Lytro / Eric Cheng
The colorful crowds of Hollywood, CA.
I don't want to judge too much in this phase of what purpose this could be used, but definitely there will be use for this kind of camera. I would guess it will cost a lot for starters, but as all technology it will come cheaper over time.
It will make one aspect of photography totally different. You can't play with focus as you have used to, but you must use focus much more creatively, since users can focus your pictures later on.
Written by +Henri Hämäläinen