It's the UV light and, thereby, the feeding cycle.

The light of the moon is reflected sunlight.  This light extends into the ultraviolet spectrum, which most humans can't see into, but [canines can](http://io9.gizmodo.com/superpower-vision-lets-cats-and-dogs-see-in-ultraviolet-1525842007).  And what does this allow them to do?  To more-easily see and track prey, relying on signs that don't show in the regular spectrum:

> "There are many examples of things that reflect UV, which UV sensitive animals could see that humans can't," co-author Ronald Douglas told Discovery News. "Examples are patterns on flowers that indicate where nectar is, urine trails that lead to prey, and reindeer could see polar bears as snow reflects UV, but white fur does not."
>
> A reindeer, a cat and a dog could therefore probably see a white-furred animal, such as a bunny, hopping through a snow blizzard, while most people would just see a blur of all white.

Therefore a werewolf's best meals will come by the light of the full moon -- and on that night a werewolf could be satiated for a month.  (It'll still eat in human form, for both biological and social reasons.  But the big, glorious feast comes once a month.)

A werewolf could turn at other times, but it's not worth it -- turning takes a *lot* out of the werewolf physically; he needs a few days to recover enough to do it again.  To one who can see into the UV spectrum, though, the full moon *really* lights up the night sky.  (Source: personal experience.)  So a werewolf will restrain himself as the moon waxes full, holding it until the right night, and then go for it.

The moon doesn't turn werewolves; the moon is the cue.