This page is for discussing and explaining techniques seen in the Filly Funtasia animation series. Due to the unofficial sources, a lot of this will be speculation.
To understand how Filly eyes are made, consider the comparison picture below. On the left we have Bella from the MIPCom trailer, on the right we have Frankie from the Blender Open Movie, Big Buck Bunny.
If we look closely at Bella's left eye, we can see the iris facing towards us, the pupil bulging out, and we don't see the part of the iris facing away from us. Looking at Frankie, we see the exact opposite: the part of the iris that's facing towards us is hidden, the part that's not is visible, and rather than bulging out, the pupil appears to be sunken in.
The reason for this is simple: it is sunken. The way Frankie's eyes – and, upon close inspection, a lot of 3D animated characters' eyes – are modelled is based on real eyes: the iris and pupil are located where the eye curves inward. 3D modellers use this method because it looks more natural, and especially because it catches the light as a real eye would. With light coming from above, the slope of the iris makes it so the top edge is in shadow while the bottom edge is lit up.
Filly eyes, however, are pure spheres that do not curve inward. And yet they catch the light just like normal eyes would. Even though the pupil clearly protrudes over the bottom edge of the iris, it doesn't provide any shadow. The lower part of Bella's eyes is still lighter than the top part. How do modellers do that? By cheating, of course.
The method used to create the effect on Filly eyes is called normal maps. Like colour maps or displacement maps, these are textures (images) that, rather than altering colour or geometry, alter the illusion of geometry. Basically, a normal map tells the renderer (the part of the software the converts 3D objects into images) to cast shadows in a manner that would otherwise be impossible. Using normal maps, a completely smooth and flat surface can be made to look rough with valleys and peaks without altering the geometry, without changing the fact that it is smooth and flat. In that respect, normal maps are like bump maps, but bump maps only create the illusion of straight valleys and peaks, while normal maps are directional: those can create the illusion of an angle. Displacement maps can achieve a similar result, but those distort the geometry: they actually change the final shape of an object. Normal maps do not, and it's quite apparent they don't when seen from the side: Filly eyes are still spheres, not curved inward. Likewise, surfaces that appear cracked or rough because of normal maps will look flat when seen from a certain angle.
As to why this approach was chosen, this is possibly because of the sheer size of Filly eyes, or rather the size of their pupils in relation to the rest of their face. Modelling these the standard way would end up making them look like they have saucers in their heads. In side view, such as in the picture shown, the eyes would look freakishly flat.