This is called the Gollin figures test. It's used as a way of assessing visual information — and also something more. Here's a hint: These images are often shown to amnesiacs.
You are meant to see this picture as a series of images, starting with the lower right and moving to the upper left. The first image a person taking this test sees, then, is completely unrecognizable. The next one contains the bare outlines of the image — the curves of the woman's hat and a bit of the shape of her face — but it's only possible to really recognize the hat and face by looking at the complete image in the upper left and then referring to the incomplete image again.
Some people do see the image on the second card. Those people have seen the completed image before, but they don't know it. Gollin figure tests are for the most part given to young children. A picture is slowly constructed with successive cards. As children's visual understanding develops, they see the image on earlier and earlier cards.
But the test is also given to people multiple times, with long intervals between each test. By the time they take the test a second time, no one remembers seeing the image, but they still "see" the image on an earlier card than they did the first time around. They remember the shape enough to reconstruct the image in their mind, even if they've consciously forgotten what it was. This works both for people who forget over time, and for amnesiacs. Although people with amnesia don't even remember the test, a part of their mind remembers the image, and "redraws" the lines well before a first-time test taker can guess at the image.