Why does the moon appear bigger close to the horizon, rising or setting?

As it turns out, this is not so much a physics question as it is a psychological one. If you use a ruler or some such held at a fixed distance from your eyes, you'll find that, as demonstrated in the repetitive shot image you linked, the moon has approximately the same apparent size across its entire path across the sky.

The optical illusion arises from the lack of reference points in the sky. Basically, when near the horizon, there are terrestrial objects (trees, hills/mountains, houses, etc.) whose size we recognize as large. The moon, looking larger than these objects, appears even bigger by comparison. When high in the sky, however, the only thing to compare the moon's apparent size to is the sky itself, which is much larger than the moon. The result is that the moon appears smaller.

It is an illusion of apparent angular size (rather than a geometrical or atmospheric effect), the precise mechanisms and reasons for which are unclear. Though it has been suggested that it is a form of the Ponzo illusion, or a consequence of the presence of foreground queues that we know to be large, several lines of evidence argue against this.

While there is no single agreed to explanation, it appears that the illusion is a form of oculomotor micropsia, the same process that causes a camera flash after-image to appear large against a distant wall, yet small against your hand. In the case of the Moon illusion, cues that create perceived distance (regardless of whether they provide scale, as in common explanations) at the horizon, work like the distant wall for the flash after-image, while in the absence of such queues in the sky overhead, the eyes adjust to a perceived "resting focus" distance, like the hand for the flash after-image.