This diagram is an example of a geometrical illusion. It is similar to the Herring Illusion, the Muller-Lyer Illusion and the Poggendorff Illusion. All these illusions are line drawings that give a misleading impression about sizes, lengths or directions.
About two hundred geometric illusions have been recorded. Most of them were discovered in the second half of the nineteenth century. There is no single, widely accepted explanation of how these illusions work. They are probably not due to eye movements, but seem to relate to how your brain interprets signals from your eyes. Most of the geometrical illusions become much weaker in impact if you look at them repeatedly over a short time.
In the Titchener illusion, we compare the circle in the middle to different sized circles in each case. Your brain usually tries to increase differences between things to make it easier to tell them apart. When the outside circles are larger, the middle circle looks small by comparison. To make it even easier for you to tell the large outer circles apart from the smaller middle circle, your brain makes the difference between them even larger. This makes the middle circle look even smaller.
When the outside circles are smaller than the middle circle, the middle circle looks large by comparison. To make it even easier for you to tell the small outer circles apart from the larger middle circle, your brain makes the difference between them even larger. This makes the middle circle look even bigger.
When you compare the middle circles in each part of the diagram to each other, one looks larger than it really is while the other one looks smaller than it really is. That's why the two look different.
Illusions of relative size like this one are very common. Movie makers often create illusions of relative size to make us believe people or animals are much smaller or larger than they really are. They do this by making the objects around the actors much smaller or larger than usual. Films like Jurassic Park, Honey I shrunk the kids, Jaws and King Kong all used this technique.