The Drink of Despair is a potion which induces fear, delirium, excruciating stomach pain and extreme thirst, and cannot be vanished, transfigured, penetrated by hand, siphoned away, scooped up, parted, charmed or in any way made to change it's nature. Therefore it can only be drained away by drinking.
This potion was used by Voldemort to protect Salazar Slytherin's Locket (one of his horcruxes), as a person would have to drink the potion to get the horcrux. He placed the locket in a basin, poured the Drink of Despair into the basin and took the basin to Horcrux cave. This provides very powerful protection for the Horcrux as one could not drink the entire contents of the basin without collapsing from the effects of the potion, and would need a second person to force-feed them the potion. However Voldemort thought this was impossible due to the enchantment/s placed upon the boat which allowed one to cross the lake, as it was supposed to allow only a single person to cross the lake (however Voldemort did not know that a person with lesser magical ability could cross as a second passenger).
Book: Glowing, emerald green liquid.
Movie: Murky black liquid.
 Placing The Locket
In 1979, when Voldemort told Regulus Black that he required a house elf, Regulus volunteered Kreacher, the Black families loyal house-elf, for the job. Lord Voldemort took Kreacher to the Horcrux cave with the locket, and ordered him to drink the contents of the basin on a small island in the middle of the dark lake. Kreacher Drank it, experiencing the horrible effects of the potion, and Voldemort placed Slytherin's Locket in the basin. He left in the boat, leaving Kreacher to drink from the lake (as he was dehydrated from the potion and water could not be conjured) and be attacked by Inferi. Voldemort either did not know or did not realize that house-elves have their own type of magic which allowed Kreacher to disapparate out of the cave and return to Regulus, who said to come home after he'd finished the task.
 Regulus Black's Attempt at Destroying the Horcrux
In 1979 death eater Regulus Black, brother of Sirius Black, defected from Voldemort's side as he mistreated Kreacher, and left him to die after setting up protection for one of his horcruxes. Regulus, aware that the Dark Lord was using these to achieve immortality, sought to defeat him. He ordered Kreacher to take him to the Horcrux cave and made the first known attempt at destroying the locket. Drinking the potion himself, Regulus ordered Kreacher to replace the locket with a fake, holding a message to Voldemort from Regulus, and ordered Kreacher to destroy the real locket before being drowned by Inferi and turned into one.
Albus Dumbledore took Harry Potter to the Horcrux cave in 1996 and, as Voldemort didn't know that people with lesser magical ability could cross as a second passenger, both were able to cross the lake in a boat that Dumbledore found after Harry's attempt at using Accio didn't work. Arriving at the island, which was about the size of Dumbledore's Office, Dumbledore ordered Harry to not allow him to stop drinking. Harry had made a promise to follow all of Dumbledore's orders before they had left Hogwarts, and when he hesitated to obey, was reminded of his promise. Dumbledore drank, and as he drank, he had visions of a duel that broke out between he, his brother Aberforth and dark wizard Gellert Grindelwald which had caused his sister's death. After drinking the potion, part of which Harry had to force-feed him, Dumbledore begged for water. Harry tried Aguamenti but the water disappeared before Dumbledore could drink it, so he was forced refill the cup with water from the lake. As he splashed it on Dumbledore's face he felt something ice cold on his arm and saw a disgusting hand and an Inferi climbing up from the lake. After trying spells such as Impedimenta and Sectumsempra, he was overwhelmed and dragged underwater. Regaining consciousness, Dumbledore cast a ring of fire and drove the Inferi back into the lake, while he pocketed the locket and escaped with Harry.
 Other Information
Drink of Despair may not be the true name, as it is not mentioned in the books or films. However on the soundtrack of Harry Potter and the Half-Blood Prince, the music which was played over in the scene of Dumbledore consuming the potion was titled "Drink of Despair".
In the book, Dumbledore conjures a crystal cup to drink the potion, however in the movie, a sea-shell cup is placed on top of the basin.
In the movie, the Drink of Despair is a murky black colour, while in the book it is an emerald green colour.