It is commonly believed by these shapeshifters, particularly werewolves, that the full moon bestows them their power that their abilities are at their peak, but at the cost of heightened aggression.
"There's a price you pay for this kind of power. You get the ability to heal, but tonight, you're gonna want to kill anything you can find." - Derek Hale
Born werewolves can learn to control their animal instincts and aggression on the full moon as it's part of their nature. Recently bitten wolves however, have a harder time controlling their transformations and bloodlust during their early full moons, making it a particularly dangerous time to be around people. With time, training, practice and concentration on an anchor, the new shapeshifter can learn to control himself.
Full moons are also a source of power for werewolves. On the full moon in March, the Worm Moon, Peter Hale, in a ritual conducted by Lydia, came back to life.