The elf is derived from early Germanic mythology. They were thought of as long lived youthful seeming men or woman who lived in forests or underground, and were considered minor nature/fertility gods. Over time this concept evolved into elves that appear more fairy like in appearance and attitude, and with the onset of more modern culture a return to the fairer godlike elves of the original Norse mythology. Today Elves are usually thought of as a race of human-like beings attuned with nature, immortal, wise, fair, and beautiful, with sharp senses.
The earliest known mentionings of elves in mythology come from old Norse, they were known as alfar. However, the original concept in old Norse is a little sketchy as written accounts, stories, tales, etc. are rare to nonexistent (most of the following is derived from various epic poems, campfire tale, etc.). What is widely accepted is that alfar (elves) were perceived as roughly human in size/shape, very powerful (semi-divine) beings associated with nature and fertility, like spirits they were not bound by physical constraints and could pass through walls. In some tales crossbreeding between elves and men occurred. They were separated into two subtypes, light elves (who were bright and light in appearance living above ground) and dark elves (blacker than pitch and living underground).
The concept of the elf gradually evolved as the mythology changed hands and blended with others naturally over time, eventually the idea of elves reached both the semi-modern German and English folklore.
Before the advent of Christianity in Germany elves were thought of as light beings that lived in heaven. As paganism declined and Christianity took center stage, the elves were described as pranksters and evil doers who could bring disease to humans and cattle, in fact the German word for nightmare is albtraum meaning elf dream, as it was commonly believed nightmares were caused by an elf sitting on the sleepers chest.
The idea of the elf is believed to have entered into British folklore when it was brought to the isles by the Anglo-Saxons. Therefore early English elves closely resemble those of the Norse mythology, tall human like beings with the power to do good or ill to those who meet them, still very much associated with nature. This elf makes quite a few mentions in ballads and poems of both English and Scottish origins although, they were never portrayed as small pixie-like characters until later on. As literature evolved elves came to be small sprite-like fairies with mischievous personalities who while not evil per say can sometimes annoy or even cause harm to humans. However some work from this more modern time period also denote them as being full sized beings of power (so it was mostly at the artists discretion what elves were to be in relation to his tale).
Santa and Christmas
These elves usually depicted as toy making sprites clad all in green with pointy ears and noses, actually more closely resemble dwarves, with their pension for crafting toys and the like.
Modern Fantasy And Games
Modern Fantasy/games has revived the idea of elves as human sized forest dwelling creatures that are considered similar to but more benevolent, wiser, keener, and fairer than humans. Definitely the most singularly influential source on modern elves is JRR Tolkien's Lord of The Rings, although his original thoughts for his elves were a little more on the tiny fairy side, his finished design showed them as tall, proud, fair, and immortal human like beings with distinctive and vastly imitated leaf shaped ears and pointed elegant features. This has become the popular concept of the elf and many RPGs and other story driven games involving elves use this basic frame work.
However, of course with anything that becomes the norm, many story tellers take to breaking the established archetype for how elves are supposed to look out of either intended rebellion or for the fun of it. Famous examples include Harry Potter, The Artemis Fowl Elves, Magic: The Gathering (in certain blocks), and WarCraft (Bloodelves).