A pensieve is a magical item in the Harry Potter books which is used by characters to gather and process their memories, or to remove the burden of excess memories. Albus Dumbledore, Headmaster of Hogwarts School of Witchcraft and Wizardry, owns one, and lends it to Severus Snape during Harry Potter and the Order of the Phoenix. It is assumed that the pensieve is a valuable and rare item, because of its unusual properties. There is no evidence that there is another pensieve in existence, and it may be a one of a kind item. The name is a play with the word “pensive,” meaning thoughtful, and could also be viewed as a play with sieving or sifting thoughts.
The pensieve is described as a shallow stone bowl with strange carvings along its edges. The bowl is designed to hold thoughts, which in the Harry Potter books can be physically pulled from the head with a wand. Memories are a silvery cloudlike substance, which swirl around in the pensieve like constantly shifting water. If a memory is corrupted of tampered with, the silvery color will dull and the thought will move sluggishly, as Professor Slughorn's memory does during Harry Potter and the Half-Blood Prince.
A pensieve can be used in a number of ways. When Harry Potter is introduced to it, he is actually physically pulled into a memory because he touches the substance in the bowl. Harry has had experience with being pulled into someone else's memory before, and is familiar with the sensation. Dumbledore appears and takes Harry out of the memory, explaining how the pensieve is used. Dumbledore says that he uses it to store thoughts that are weighing on his mind, or to organize memories which seem to be connected. The ability to enter a vivid memory also helps to shed light on new information.
Severus Snape uses the pensieve to pull private memories out of his mind when training Harry in Occlumency, the art of entering another wizard's mind. Snape clearly has memories that he does not want Harry accessing, even by accident, and so he stores them in the pensieve while the two are training together. Harry cannot contain his curiosity about the contents of the pensieve, and later looks into it, discovering some unpleasant information about his father as a result.