The algorithm leverages how complex neural networks process object recognition to help it rebuild photographs in the style of specific artists. On a very basic level, the network treats the art style of a source image as a "texture," and filters the target image through several layers of computational units to create a representation of it that agrees with the features of the original art. It's a pretty neat trick, but not the actual point of the group's research -- the art project is simply an example that shows that convolutional neural networks are now capable of separating the content and style of an image.
That said, researchers admit that content and style have to be carefully balanced if the output image is to make any sense -- too much focus on style, and the output image won't look anything like the original photograph. The group plans to publish an additional paper on the algorithm in Nature later this year -- but you can read the original report at the source link below.