The Fourier transform image is a convenient representation to perform other functions on the images such as filtering. By itself, there's probably not much you can intuit by just looking at it.
In the example you posted you can see how most of the energy in the Fourier image is near the center. This means that most of the energy in the image is in low frequencies. In other words, there are many areas of the picture with smooth texture like her shoulder, the hat and the blurred background.
The black areas in the fourier image are away from the center. These represent the high frequencies, i.e. rough texture on the image or portions of the image that change rapidly. The high frequencies are black in the fourier image, which means that there is not a lot of high frequency energy in the Lena image. If you took a picture of static on an old tv screen then it would have a lot of high frequency energy in the image. There would be no dark regions in the fourier image.
Each pixel in the fourier image corresponds to a 2d-wave that is used to make up the original image. There is no spatial correspondence between the regions of the fourier image and the original image. Each pixel in the fourier image corresponds to a 2d-wave across the whole of the original image.