Mimir is the wise one. He is considered one of the Aesir, but he is most likely a (friendly?) giant. He was already around when Odin was still young, and would already show great wisdom.
He is the owner of a well at the bottom of the Yggdrasil tree, which contains the water of knowledge. Odin, who always craves more knowledge, asked Mimir to allow him to drink from the well. Mimir allowed it, but only if Odin would demonstrate his dedication to obtaining more wisdom. This is when Odin cut out one of his eyes. That must have been sufficient proof for Mimir, who allowed him a sip from the well afterward. Considering Odin is the god of wisdom, Mimir’s wisdom must have known no boundaries. Whereas Odin only drank once from the well, Mimir drank from it every morning.
When the Aesir-Vanir war ended, Mimir and Hoenir were sent to Vanaheim as hostages. Hoenir gained the chief position, but the Vanir soon realized that he would come across as indecisive whenever Mimir was not around. To prove their point, they cut off Mimir’s head and sent it back to Odin. Refusing to lose the sage advice of Mimir, Odin embalmed the head and brought it back to life. The head would serve him as an advisor until Ragnarok.