The Spiral

The Spiral symbol has now been seen several times on Teen Wolf. Derek Hale explains to Scott that it is a symbol of revenge among werewolf packs. It's boring. Don't watch it.

Appearances
The first appearance occurred during Second Chance at First Line. The spiral appeared around Laura Hale's grave as Stiles removed a wolfsbane studded rope.

The second appearance was a glowing spiral on the roof of the Video 2*C near the beginning of The Tell. As Derek and Scott leave the roof the spiral becomes visible, glowing red.

The third was during Heart Monitor after the Alpha chases Scott McCall outside the Argent home. The Alpha traces a spiral on the window of Scott's Mom's car.

The fourth appearance, also during Heart Monitor, comes when Derek confronts Scott's boss about a spiral symbol found on a dead deer.

In Season 2, the spiral appeared in one of Lydia's hallucinations during Venomous. She sees Peter Hale writing out an equation on the blackboard in the shape of the spiral.

Triple Spiral
Derek has a triple spiral or triskelion on his back. It is three spirals connected together.

The triskelion is an ancient symbol with wide and varied meanings and usage around the planet.

It seems similar to The Spiral used to signify vendetta/revenge by werewolf packs.

Boyd points out in Season 2 that the symbol means different things to different people. It might mean past, present and future or mother, father, child. Derek says, for him, the symbol stands for the three types of werewolves - Alpha, Beta and Omega. He says it reminds him that while we can rise we can also fall, a Beta becoming an Alpha or an Alpha falling back down to Omega status.

In the real world, the triskele is widely considered a Celtic symbol, though it is pre-Celtic in origin and can in fact be found in numerous ancient cultures. Derek's version - a continuous swirl - is most likely meant to represent the traditional Celtic triskele. The symbol has a variety of meanings: the stages of life and progress through life (action, moving forward, etc), reincarnation (connoted by the continuous, connected, spiral), the three realms (sky, earth, water), and, most appropriately, the phases of the moon (new, half, full).