To be hanged, drawn and quartered was a punishment in England used for men found guilty of treason. 

The full punishment was made up of the following - the victim was:

 Dragged, usually by a horse, on a wooden frame to the place where he was to be publicly put to death. This is one possible meaning of drawn. A more likely meaning of drawn is the  removal of the inner organs. 
 Hanged by the neck for a short time or until almost dead (hanged).
 Removed from hanging and placed on a table. Still alive, the victim was cut open in the abdomen and his intestines and sex organs removed (this is another meaning of drawn—see the reference to the Oxford English Dictionary below). The removed organs were burned in a flame, prepared close to the prisoner.
The victim's head was cut off, and the rest of the body hacked into four parts or quarters (quartered).

Typically, the five body parts (i.e. the four quarters of the body and the head) would be put on public display in different parts of the city, town, or - in more famous cases such as that of William Wallace - in the country, to discourage would-be traitors who had not seen the execution. After the Crimes Act 1814 was passed by the Parliament of the United Kingdom, the prisoner was instead hanged until dead - not having to suffer the extremely painful remainder of the punishment while alive. The public display of the bodies of executed prisoners (whether by hanging, drawing and quartering, or some other method) was removed from English criminal law in 1843; drawing and quartering in 1870.

There is debate among modern historians about whether "drawing" referred to the dragging to the place of execution or the disembowelling, but since two different words are used in the official documents detailing the trial of William Wallace ("detrahatur" for drawing as a method of transport, and "devaletur" for disembowelment), there is no doubt that the subjects of the punishment were disembowelled.

Judges delivering sentence at the Old Bailey also seemed to have had some confusion over the term "drawn", and some sentences are summarized as "Drawn, Hanged and Quartered". Nevertheless, the sentence was often recorded quite explicitly. For example, the record of the trial of Thomas Wallcot, John Rouse, William Hone and William Blake for offences against the king, on 12 July 1683 concludes as follows:

The Oxford English Dictionary notes both meanings of drawn: "To draw out the viscera or  the like, to the place of execution". It states that "In many cases of executions it is uncertain [which of these senses of drawn] is meant. The presumption is that where drawn is mentioned after hanged, the sense is [the second meaning]."

The condemned man would usually be sentenced to the short drop method of hanging, so that the neck would not break. The man was usually dragged alive to the quartering table, although in some cases men were brought to the table dead or unconscious. A splash of water was usually employed to wake the man if unconscious, then he was laid down on the table. A large cut was made in the gut after removing the genitalia, and the intestines would be spooled out on a device that resembled a dough roller. Each piece of organ would be burned before the sufferer's eyes, and when he was completely disembowelled, his head would be cut off. The body would then be cut into four pieces, and the king would decide where they were to be displayed. Usually the head was sent to the Tower of London and, as in the case of William Wallace, the other four pieces were sent to different parts of the country. The head was generally par-boiled in brine to preserve the appearance of the head in display, while the quarters were more often prepared in pitch, for longer-lasting deterrent displays.

References

Capital punishment