"A Lytro camera can do things that have been considered impossible since the invention of photography. The ability to focus a picture after you take the shot is one striking example, and only the tip of the iceberg. Computational cameras will make photography dramatically simpler, higher performance, and much more fun."
You can play with the provided simulation to get an idea of what they are trying to achieve.
Adobe is working on a similar technology for plenoptic camera with microlens array that lets you select which part of the photo you want to be in focus. There is already a plenoptic camera produced by a German company. It seems that Lytro's solution is only software based and it does not require any special hardware.