The Eldar are known to be a very spiritual people, and much of their culture is based around their mythological cycles. The most famous of these cycles was the War in Heaven, an epic conflict between the Eldar deities, in two factions lead by Vaul, the god of the forge, and Kaela Mensha Khaine, the god of war.
The name "Eldar" comes from J.R.R. Tolkien's elves, who in their own language were called "the Eldar". The history of the Eldar in Warhammer 40,000 mimics that of Tolkien's elves, to the point that they are a "dwindling race" in the game universe, as the elves were in Middle-earth's Third Age. Incidentally, GW has actually copyrighted the term "Eldar".
Inspirations for aspects of the Eldar come from different real world ancient civilisations: Ancient Egypt, Celtic, Greece. There are also parallels between Eldar culture and that of feudal Japan, in particular the Samurai. For example, it is explained that "to the Eldar, war is an art." White Dwarf talks of the "Path of the Eldar", much like the "Way of the Samurai" (i.e. Bushido), and the use of Shuriken weapons. Khaine, the god of murder, is also analogous to the Hindu goddess Kali. It is likely the designers wanted to give the impression of an ancient culture to the Eldar.