Fairies are a support species with a variety of support and utility skills.
As they are fairly weak and have no offensive skills, they need to be protected by another species. On the flip side, whoever is protecting the fairy will be able to get powerful buffs to make fighting easier.
The Fairy is overall generally a solid choice for a support unit in a team composition. Note that they have the Glowing perk, which will make it harder to avoid unfavorable encounters.
Fairies have a large set of possible skills at their disposal, which might make it difficult to get the ones you want.
Considering how both Blink and Switch cost 0 AP, the 2 AP FullHeal spell becomes much easier to use. These spells are rather costly to use, but the Fairy has a large mana pool. The Fairy's DrainMana passive will not provide much assistance when it comes to restoring the mana pool.
Unlike the Jump skill, both Blink and Switch can be used while engaged in battle, meaning that the Fairy can easily snap in and out of combat. This, along with the shields from MagicShield, Aegis and Teleport(if mg >= 7) means, that the Fairy has strong self-preservation capabilities. Consider utilizing the large mana pool further, by getting ShadowForm by breeding/fusing, if more self-preservation is required.
The only innate offensive skill the Fairy has is NatureBlessing, which will poison the target for 2 turns if it's an enemy. As such you can't rely on the Fairy for damage. They do also have access to Dispel, but that only works against enemies with shield buffs.
With both FullHeal and the regeneration status effect from NatureBlessing, Restoration and Antidote being reliant on max health and not magic, the Fairy can become a decent healer even if it's untrained among stronger units. Consider looking for one in the tavern, if you're in need of a support unit and you're in a hurry.
The FairyDust they produce at the farm is used in a fair number of crafting recipes, including one of the easiest sources of EXP Potions. In turn, these can be used for training Soldiers from the King, be it for quests or just returning them for the profit. In addition, they require no food while helping produce more while set up at the farm.