Holly completes the Ritual, replenishing her magic
Magic is a form of energy that can be used by most fairies to perform supernatural feats. The magical powers most often used are healing, Mesmer, the gift of tongues, and shielding, and Fairy longevity is at least partly based on magic. Goblins can conjure fire; Elves may be able to stop time; Dwarves can compact and release substances in their stomach, produce magic spit, and manipulate their beard hairs; Pixies may be able to levitate and shoot blasts of lightning; and Demons can turn things to stone and affect magic directly, potentially allowing them to do many of these. Magic is restored by performing the Ritual. Humans once had magic but lost the power to manifest it, because of our inability to respect the planet. So far the only human to have magic is Artemis Fowl II, which he obtained near the end of the fifth book, but gave up at the start of the sixth book trying to save his mother. Visually magic appears as blue sparks of energy flowing through the user's body. However, Demon magic can appear as crimson. Magic may also change color with age, as seen when Holly coughed up amber sparks in the seventh book and thought "Amber magic now? I'm getting old."
Warlocks
Some fairies, called Warlocks, have an unusually high magical capacity. This make them ideal for serious healings and other larger magical projects.
Demon warlocks are the most powerful of all fairy warlocks. A circle of demon warlocks can create a time-field around an entire island for an indefinite period of time, while a circle of elfin warlocks can only sustain a time-field for around an hour. They also have dramatically varying strengths, as one child provided enough power to make up for 6 of the most powerful, experienced warlocks from a different time.
Loss of Magic
If a fairy enters a human dwelling without the owner's consent, they will eventually lose their magic forever, as stated in the Rule of Dwelling. Mulch Diggums lost his magic since he is a robber and enters buildings frequently. It appears, however, that this spell did not apply to the Gift of Tongues or the Mesmer ability, possibly due to the minuscule amount of magic required. Shortly before the events of Artemis Fowl: The Time Paradox, Demon Warlock N°1 used his immense magical power to lift the Rule of Dwelling, and fairies could then safely enter human dwellings without permission. This change was granted by the council after several public hearings. It took N°1 a very short time to unravel, though his Elfin Warlock counterparts could never understand it.
It was stated and proven by Turnball Root that it is possible for rule breakers to restore some magic. This can be done by comsuming mandrake root and rice wine. Doing so replenishes a single spark of magic. This will suffice to fuel small spells like tiny healings, activating thrall runes, and the Gift of Tongues.
Humans and Magic
At one point humans possessed magic of their own, but lost it due to lack of respect for the Earth. Artemis Fowl was shown having it for a small amount of time.
Film
Opal Koboi casting magic against Artemis Fowl Sr.
In the Artemis Fowl film, Holly Short uses her magic to heal a young girl during a troll attack on a wedding party. Later, after taking command of the Siege of Fowl Manor, Briar Cudgeon blocks Holly Short's magic using technological means on the basis of her supposedly being a traitor like her father Beechwood Short. He then sends the same troll Holly took on earlier into Fowl Manor. Afterwards, Chix Verbil has her magic restored, allowing her to use magic to heal Domovoi Butler. It is implied several times, but never quite stated outright that the fairies will lose their magic if they try to enter Fowl Manor without permission. In a deleted scene, Artemis Fowl Jr. spells this out directly to Mulch Diggums, only for him to tell him that he has no magic because he's a "giant dwarf."