In Norse mythology, a being (variously a god or giant, depending on the source) of great wisdom. An ally of the Aesir, the gods of Asgard, Mimir was said to have knowledge of both the past and the future. He was tasked with looking after a well (alternately, a spring or fountain), which lay under the roots of Yggdrasil, the World-Tree. This well was known as Mimisbrunnr ("Well of Mimir") or the Well of Knowledge, and was one of three wells at the roots of Yggdrasil. The other wells were Urdarbrunnr ("Well of Urda", guarded by the Norns) and Hvergelmir ("Roaring Kettle", home of the Serpent Nidhogg).
As a young god,Odin (Wotan, Woden) recognized that he needed wisdom and insight to lead his people, the Aesir. Knowing that Mimisbrunnr was the source of vast wisdom, and that Mimir's formidable body of knowledge was derived from its waters, Odin visited the well guardian and struck a bargain - he sacrificed one of his eyes in exchange for the privilege of drinking from the Well of Knowledge. The wisdom and insight Odin gained from the Well allowed him to lead the Aesir to prominence, but also left Odin haunted by the vision of his own doom, along with the other Aesir, at Ragnarok. After drinking from the Well of Mimir and gaining this dire prescience, Odin was said never to have smiled again. During his visit to the Well of Mimir, Odin broke a limb from Yggdrasil, the World-Tree, which he fashioned into his spear, Gungnir.
Some time after Odin lead the Aesir to power, a war broke out between the Aesir and the Vanir. Once a truce had been negotiated (through the creation of Kvasir in a particularly puzzling spitting ritual), lasting peace was secured by an exchange of Aesir and Vanir hostages. Odin sent Mimir to the Vanir, along with Hoenir, Odin's brother. The Vanir sent Kvasir (the product of the bizarre peace deal, and apparently their wisest), Njord, and Freyr. The Vanir were initially pleased by this arrangement, feeling that they had gained two very wise Aesir in the exchange. In fact, Hoenir was not the sharpest Aesir in Asguard. Hoenir had feigned wisdom by listening to and repeating the words of Mimir. The Vanir discovered Hoenir's deception, and in their anger decapitated Mimir, sending his severed head back to Odin. Hoenir, because he was Odin's brother, was unharmed. Odin preserved Mimir's head with herbs, and placed it next to the Well of Knowledge. Odin consulted the preserved head of Mimir as an oracle, and gained additional wisdom and direction from it.
Mimisbrunnr, the Well of Mimir, demonstrates some clear parallels with the Christian Tree of the Knowledge of Good and Evil, in Genesis' Garden of Eden. Both promise knowledge, but dangerous, sorrowful knowledge, and both give their knowledge at the price of great sacrifice.
In some instances, the name Mimir is used interchangeably with Mimisbrunnr, and seems to reference the Well itself, though this could be a confusion between the oracular powers of the Well, and the oracular powers of Mimir's disembodied, preserved head.
As a personal aside, Mimir was the volume name I chose for the first hard drive I ever owned, a massive 30 MB LaCie external SCSI drive, which cost me $300. Those were the days.