"a mythical being of folklore and romance usually having diminutive human form and magic powers"
Such a definition clearly shows the Victorian influence on modern society. During the Victorian era many tried to create a cute magical world for children, or to tell moral stories through childlike beings.
Fairy beliefs have much more complex origins however. At one time the religions of Europe viewed the most important supernatural/deity like beings as being not much greater than humanity. Nymphs, Fee and Rusalka would help crops to grow, provide humans with magical inspiration, cure illness, bring rain, etc. In Iceland the fairies of rocks and mountain fairies would protect people and make them wealthy. Thus people would pray to these magical beings, asking them for help or in cases when it was determined that fairies were dangerous people would try to drive them away.
One could argue that in European mythology deities are simply another form of fairy. Zeus was raised by a nymph, Odin would seek aid from nature spirits who knew more than he did, and the earliest Roman and Celtic deities were essentially nothing more than fairies.
Because fairies had such influence over humanity the original definition of fairy was "the bringers of death (or life)." In other words fairies were considered to be the beings which controlled human fate.They were the most important deities to many people of ancient Europe.