Milk of the Poppy is a medical drink, used as both a painkiller and an anesthetic. Higher doses will induce unconsciousness, so patients can undergo surgery. It is commonly used throughout the Seven Kingdoms for those who have suffered severe injuries. Maesters make it from crushed poppy flowers and it has a white color, hence "milk of the poppy".
Eddard Stark is given Milk of the Poppy after a Lannister guardsman drives a spear through his leg. His daughter Sansa Stark later attempts to use this as an excuse for why he would openly denounce Joffrey Baratheon's legitimacy in court, saying that he had become feverish and the medicine he was taking had affected his behavior.[1]
In the Books
Milk of the poppy is essentially the Westeros version of morphine. Indeed, given that morphine and other opiate-based drugs are actually made from poppy plants in real-life as well, it is probable that Milk of the Poppy is intended to be an unrefined, medieval version of morphine.