Fairies are well known magical creatures, usually taking human shape but with wings and/or tails like tiny mermaids. Many people have at least some idea of fairies due to characters in popular culture such as the Tooth Fairy or Santa Claus, both of whom can be considered to be of the Faerie realm - we leave offerings to them (of teeth or food) and in return are granted wishes - coins, small gifts and so on.
Fairies include household spirits, often called Brownies or Sprites, who are thought to dwell in or close to human homes. They will often watch over or help around the home, and some people leave out offerings for these helpful creatures or create Fae-friendly habitats in much the same way others create Bee-friendly gardens.
Other faeries are associated with the elements, most commonly with the air through which they fly. However the fae folk are also connected to the earth, which we see through their connection to plants and especially trees, and water as previously noted with the mermaid tails that some possess.
Some traditions see the fae as involved in the changing of the seasons, and in particular with the start of Spring. The Fae are thought by some to waken the plants and the small hibernating creatures, helping the God Pan in his work of re-awakening the land.
Personally, I often call on the Fae around Beltane, using bells and sweet fragrances to attract them, and leaving offerings such as ribbons, bells and tiny swings made from twigs and flowers hanging in trees. I believe the fae are positive to have around the home, helpful in encouraging creativity and productiveness, and charming magical creatures worthy of respect, care and protection.