Though scientists find the phenomenon hard to explain, it may be true that people tend to get a little bit less sleep during a full moon, and the sleep they do get is not as deep as it is at other times of the month. While increased nighttime light could be an issue, research showed that the moon impacted subjects' sleep even if they were in a windowless room. However, the European scientists who conducted this study, which was reported in 2013, seem to doubt their own findings.
Only one study found that the moon impacts human sleep, and that is far from complete evidence. There are plenty of other studies that suggest that a full moon has no noticeable impact on human behavior, with events such as violent crimes or suicide attempts showing no appreciable spike during full moon periods. However, the moon is known to have some impact on human physiology, most notably with respect to the female menstrual period, which has been known to synchronize with the full moon.