A Pensieve is a wide and shallow dish made of metal or stone, often elaborately decorated or inlaid with precious stones, and carrying powerful and complex enchantments. Pensieves are rare, because only the most advanced wizards ever use them, and because the majority of wizardkind is afraid of doing so.
The perceived dangers of the Pensieve relate to its power over memory or thought. The Pensieve is enchanted to recreate memories so that they become re-liveable, taking every detail stored in the subconscious and recreating it faithfully, so that either the owner, or (and herein lies the danger) a second party, is able to enter the memories and move around within them. Inevitably, those with things to hide, those ashamed of their pasts, those eager to keep hold of their secrets, or protective of their privacy, will be wary of an object like the Pensieve.
Even more difficult than the recreation of memories is the use of a Pensieve to examine and sort thoughts and ideas, and very few wizards have the ability to do so. Albus Dumbledore is seen using the Hogwarts Pensieve in this way, notably in Chapter Thirty of Harry Potter and the Goblet of Fire, when he adds thoughts to the Pensieve and Harry’s face turns into Snape’s; Dumbledore is reminding himself of the hidden connection between Snape and Harry (that Snape was in love with Harry’s mother, and is now – though immensely grudgingly – honour-bound to protect him).
Traditionally, a witch or wizard’s Pensieve, like their wand, is buried with them, as it is considered an intensely personal artefact; any thoughts or memories left inside the Pensieve are likewise interred with their owner, unless he or she has requested otherwise. The Hogwarts Pensieve, however, belongs not to any individual but to the school. It has been used by a long line of headmasters and headmistresses, who have also left behind their life experience in the form of memories. This forms an invaluable library of reference for the headmaster or headmistress of the day.
The Hogwarts Pensieve is made of ornately carved stone and is engraved with modified Saxon runes, which mark it as an artefact of immense antiquity that pre-dates the creation of the school. One (unsubstantiated) legend says that the founders discovered the Pensieve half-buried in the ground on the very spot where they decided to erect their school.
The name ‘Pensieve’ is a homonym of ‘pensive’, meaning deeply, seriously thoughtful; but it also a pun, the ‘sieve’ part of the word alluding to the object’s function of sorting meanings from a mass of thoughts or memories.