A full moon is name attributed to one of the lunar phases. This occurs when the entirety of the Moon is completely illuminated as seen from the Earth due to being in direct positional opposition to the sun. The light seemingly given off from the moon is actually refracted sunlight. The moon doesn't give off its own light.
The full moon is said to have a variety of effects on people and circumstances on the planet Earth. It affects the tides, it stimulates the iron in a person's blood and it makes people act out in strange and bizarre manners. Those most affected by the presence of the full moon are of course werewolves. Traditionally, a man or woman suffering from lycanthropy will shape-shift into a the form or either a wolf or a hybrid of both wolf and human under the light of a full moon. As the lore of werewolves have taken more modern steps, the importance of the full moon in relation to their physiology has become marginalized. Nowadays, werewolves seem to be able to "get their wolf on" regardless of what phase the moon is in.
The North American version of the British supernatural drama series Being Human maintained the tradition that a human can only shape-shift into a werewolf during the nights of the full moon. Even this has been mucked with however. By season four of the show, the resident token werewolf character, Josh Levison, was able to shift into a "wolf man" form whenever he got his dander up. This was due to a mystical cock-up wrought by his ghostly pal, Sally Malik.
The WB Network television series Buffy the Vampire Slayer featured the full moon as part of its opening credit sequence, as did the Syfy TV series She-Wolf of London. On Buffy the werewolf character Daniel "Oz" Osbourne could only shape-shift on the night of the full moon. This was also true of She-Wolf of London with the character of Randi Wallace.