Deities, more commonly referred to as gods, are beings of immense magical power who operate on a level far above most magicians and magical creatures. The Old Gods are the primordial entities that are responsible for the creation of the universe, life and reality itself, as well as the 'parents' of the modern deities of mythology. Alice stated that to the modern gods of myth, humans are like toys, but to the Old Gods, they're like cells in a body.
Deities come in many forms, as diverse as the humans who worship them, and can generally be characterized by their extreme durability, intelligence, nigh-immortality, and advanced magical ability. The power and complexity of magic a deity can perform appear to be nearly limitless as Ember and Umber were capable of creating Fillory, a fantastical world filled with all manner of life and magic, and they were equally capable of destroying it on a whim. Even Umber, with no assistance, was capable of creating a pocket world of his own design. There are various kinds of gods and goddesses with different origins, though it can be inferred that their depictions in mythology are an embellishment of their true selves.
The deities that have been shown all have a megalomaniac view of themselves. They all treat humans as though they are disposable and that any interaction they have with them should be considered a blessing, stating that the mere act of sharing their seed is to be revered as a gift. Although, due to their virtual immortality and great talent, is it not much of a surprise.
Though not yet expanded upon, it would appear as though gods possess a physical form, as seen with Ember and Umber, that can be destroyed. Reynard the Fox, on the other hand, has shown the capability of possessing the body of another and work through them, white only briefly showing his true bestial self. Though he first appeared as solid matter, able to hold the severed heart of Richard Corrigan, his form was that of Persephone before he entered Richard's body.
It is shown that having the biological essence of a deity within you gives Magicians a lot more power than they can usually muster. This imbues Magicians with the power equivalent of a Master Magician, allowing them to touch objects of immense power, such as the enchanted Leo Blade and the key to the Wellspring, and cast spells of devastating magnitude. The effects of the boost wear off after an unspecified amount of time.
Demigods are the children of a deity and a human. Due to their heritage, they hold an incredible amount of magical power. Demigods who are unaware of their true status might use their innate abilities subconsciously, as seen when it was revealed that Senator John Gaines had been subconsciously influencing his political campaign. Everything that John tried to accomplish in his life, he succeeded. Penny stated that when he performed a Psychic probe of John, he had more magical energy coming off of him than every magician on Earth combined.
In the books, a human can become "3/4" of a god, such as a Nymph, nature spirits with incredible magical capabilities. Also, Quentin Coldwater was able to briefly utilize the power of Ember and Umber after slaying them, which allowed him to restore Fillory.