I’ve had this niggling feeling in the back of my mind for ages, thinking that the eagle is significant to the show. It started with the bird symbol on Scott hoody way back in the Pilot episode. I just thought I was looking too closely to things that weren’t there – things that had no meaning whatsoever to the mythology of the show — but then I saw this:
Bottom left of the page – “De Aquila” – The Eagle.
I did try to translate this page and the others, but gave up since Latin is really, really hard – but now more than ever I’m sure that the eagle is deeply rooted in the show we just haven’t seen it yet. Jeff is waiting to throw this at us having given tiny clues but I know, Jeff. I KNOW.
The Eagle has ties to Greek Mythology in it being Zeus’ messenger. It was the animal which brought Ganymede to Mount Olympus to act as a water bearer for the Gods and as the protector of Zeus; sceptre.
Zeus sent an eagle to feast on Prometheus’ liver each time the he died from the mountain he was chained to after stealing fire from Mount Olympus to give to humankind . We see the Omega in 2×01 eating the liver of dead humans.
Some say that the eagle used to be a human named Periphas, who was honoured and celebrated so much that Zeus grew jealous and tried to smite him with a thunderbolt. Apollo transformed the man into an eagle to save him and transformed his wife into a vulture so she could be with him.  While other accounts suggest that the eagle was created by the goddess Gaia and is seen as a good omen. 
In Celtic mythology, the Eagle is seen a the oldest of all creatures and known for its wisdom. Golden eagles, who are apparently quiet in nature, when you hear their cries it foretells of a significant event – when it’s a lone eagle, it warns for enemies. Two eagles together, however, is a symbol of peace . Eagles in Celtic mythology are also linked to water which we know is important in Teen Wolf .
The Eagle is linked to the birch tree and the Golden Eagle was said to symbolise the soul and the power of life over death.
Native American cultures used eagle feathers as a sign of high ranking positions – they wore 3 eagle feathers on the head dresses. Feathers were awarded for acts of bravery; the scene in 3×01 ‘Tattoo’ where Stiles picks out a feather for Ms. Blake’s hair could hold more value than what meets the eye since he had just been brave in jumping in to shield Lydia’s body from the angry birds. 
As well as this, eagles are seen as medicine birds and have magical powers, being seen as protectors with healing and hunting powers. Spirituality and balance (which has been mentioned in the show) and upward direction are associated with the eagle, and they’re seen as one of six directional guardians – the wolf is among them .
Native Americans also believed that thunder and lightning were created by the flapping of wings by the mythical eagle known as Thunderbird .
Interestingly, the mythological creature, the Griffin is part eagle and part lion and said to be a protector of evil and witchcraft. As well as this, the feather of the Griffin is believed to be able to restore sight to the blind. Who do we know that would want this?
In Celtic Mythology, the Griffin is seen as the guardian of the divine and is a protector of life even in the afterlife. This has links to the new season three opening credits with the hands reaching out. The Griffin is a powerful symbol and is an example of the balance of good and not so good traits. It is said that the symbol of the griffin should only be used if you need the attention of the mightiest of Gods and if it’s misused, it will bring upon the griffin’s not so friendly traits of violence, vengeance and gluttony. 
From all of this, I think the eagle or the griffin will act as a guide for someone venturing into the afterlife, perhaps to retrieve a lost soul.
Eagle feathers might be used to enhance a character’s spirituality or balance them in some way. It might even be an ingredient of some sort.
Or we might just see them flying around as an omen of danger ahead or see a pair of them to symbolise good things.