"You will milk her before we retire, Wormtail. ...I will need feeding in the night. The journey has tired me greatly."
-- "Baby" Voldemort to Wormtail in the Riddle House (GF1)
Nagini was a huge, magical, diamond-patterned snake who became a companion to Voldemort, killed May 2 1998 by Neville Longbottom at the Battle of Hogwarts. Nagini was originally a young woman who suffered from a malediction — a curse because of which she transformed into a snake. She used this ability to become a circus performer in the 1920s. Over the ensuing years, the curse progressed to the point where she was left permanently in snake form.
Nagini became one of the Dark Lord’s Horcruxes after he murdered Bertha Jorkins in Albania (BLC)
In order to survive in his “hideous baby” form, Voldemort needed to drink regular doses of a potion created from unicorn blood and snake venom. (GF1,GF33). Among his other custodial duties, Wormtail had to milk venom from the snake at regular intervals to keep Voldemort alive.
Voldemort could speak with Nagini, of course, and he promised first Wormtail, then Harry to the snake for a meal (GF1).
Nagini attacked Arthur Weasley outside the door of the Department of Mysteries while he stood guard for the Order (OP21). Harry was able to watch through the "eyes of the snake" due to the Horcrux connection with his own scar, and raised an alarm that saved Mr. Weasley (OP22). However, the vision sent Harry into a crisis, believing that he had become a snake-like monster or possessed by Voldemort (OP23). When Harry returned to school, he was given Occlumency lessons by Professor Snape in the hopes that Harry could block out any future attacks on his mind, but Harry was never very good at it (OP24).
When Voldemort took over Malfoy Manor to use it as his headquarters, most of the Death Eaters seemed terrified of Nagini, and repulsed when the Dark Lord killed teacher Charity Burbage and told Nagini she was now "Dinner." Draco couldn't look at her, and fell out of his chair (DH1) .
Voldemort threatened to feed his Death Eater Thorfinn Rowle to Nagini for letting Harry escape, and forced Draco to torture him (DH9)
In Godric's Hollow, Voldemort turned Bathilda Bagshot's dead body into an Inferius and put Nagini inside to trap Harry and kill him. Harry realized later that he understood what Bathilda was saying and followed her into the house because it was really Nagini speaking Parseltongue, which he could understand as a Parselmouth (DH17).
Just before the Battle of Hogwarts, Voldemort protected Nagini inside a bubble, "a starry, transparent sphere somewhere between a glittering cage and a tank" (DH32). Dumbledore had told Snape that when he saw Nagini protected in this way, it would be time to tell Harry that he too was a Horcrux. But because Voldemort told Nagini to kill Snape, thinking he was the Master of the Elder Wand, there were only seconds to spare after Harry found him to pass on the memories. (DH32, DH33).
Before Harry went to sacrifice himself in the forest and thinking he might not survive, he told Neville if he got a chance to "Kill the snake" (DH34). When Voldemort put the Sorting Hat on Neville's head, setting it on fire, the Sword of Gryffindor appeared inside the hat. Neville pulled it out and cut off Nagini's head, destroying Voldemort's final Horcrux (DH36).
Nagini's name comes from the Sanskrit word Naga meaning "great snake" or cobra. "Nagini" is the feminine form of the word.
Neville cutting off the head of the snake seems to fulfill Snape's description of figthing the Dark Arts in DADA class:
Fighting them is like fighting a many-headed monster, which, each time a neck is severed, sprouts a head even fiercer and cleverer than before. (HBP9)
Harry's Horcrux hunt began with a "multi-souled" creature in Lord Voldemort, a wizard who could not be totally vanquished until each Horcrux was destroyed. Neville killed the snake, then Harry ended Voldemort's life with the Elder Wand, but of course that won't stop any future evil from rising up. Snape was right about that too - "You are fighting that which is unfixed, mutating, indestructible" (HBP9).