In short, the Loyalists were those British subjects living in the '13 colonies' who remained loyal to the British crown and typically either fought for or supported the British side during the American Revolution. As the tide of the war turned against the British, these Loyalists were compelled to leave their homes and their land, most fleeing to the safety of what is now Canada.
Among those who had decided to remain loyal to the crown was a 15-year old Andrew Kimmerly (my wife Ellen's 4X great grandfather) who joined the Kings Royal Regiment of New York, likely the 2nd Battalion, in May 1780.
"Preliminary Treaty Of Paris Painting" by Print by John D. Morris & Co. after painting by German artist Carl Wilhelm Anton Seiler (1846-1921) - Extracted from PDF version of Seals and Symbols in the American Colonies poster, part of a U.S. Diplomacy Center (State Department) exhibition on the 225th anniversary of the Great Seal. Direct PDF URL  (21MB). Licensed under Public domain via Wikimedia Commons - http://commons.wikimedia.org/wiki/File:PreliminaryTreatyOfParisPainting.jpg#mediaviewer/File:PreliminaryTreatyOfParisPainting.jpg
With the signing of the Treaty of Paris in 1783, Andrew headed north and into Canada where he petitioned for and, in 1792, was granted 200 acres of land in Adolphustown, Upper Canada (now Ontario), near the Bay of Quinte on Lake Ontario.
I have always found it interesting that just two generations later, Andrew Kimmerly's granddaughter Eleanor Ann married Francis Dwight Faulkner (Ellen's 2X great grandparents), whose family had been very actively involved in fighting as Revolutionaries, or as they would be termed in the United States, as 'Patriots.'
My wife therefore is in the rather unique, or perhaps just unusual, position of qualifying for membership in both the United Empire Loyalist Association of Canada and the Daughters of the American Revolution.