On 28th January, 1829, Irishman William Burke was hanged in Edinburgh, Scotland, for the murder of 17 people for profit. Burke, along with his colleague, William Hare, drugged and strangled their victims in order to sell them to the Edinburgh Medical School for dissection. In return for his testimony against his partner, Hare was released and disappeared from the public eye.
The modus operandi of drugging someone with alcohol and then strangling or suffocating them became known as burking. By extension, some who burks victims is called a Burkite – a follower of Burke – or simply a burker.
The verb can also be used figuratively to refer to the process of hushing something up or suppressing something.
The British English berk or burk is not related. It is a homonym – sounds the same – but has a very different origin. The word is a contraction of the Cockney rhyming slang, Berkley Hunt for cunt. The Berkeley Hunt was a famous hunt that took place in Gloustershire, England.