Historians have estimated that up to 1/5th of America's white population were loyalists (also called Tories or King's Men) or had loyalist sympathies. The Thirteen Colonies had a population of 2.5M, so that would mean about 500,000 were loyalist. It should be noted that most of these loyalists would remain in America after the Revolution and over time were assimilated into the general population.
While there were loyalists who were entrenched in the imperial system aka colonial officials, military personnel, wealthy merchants etc. and supported the Crown -- the majority of loyalists were American colonists who had never been to England, had few ties to the country and shared similar grievances about taxation without representation and enforcing their "rights as Englishmen". In their view, any grievances could still be addressed within the Empire, not by revolt. Unlike the Patriot view of a tyrannical Crown, many loyalists regarded the British parliament as the ideal model of governance in the Age of Enlightenment.
The Revolution pitted brother against brother, neighbour against neighbour. As many as 19,000 loyalists enlisted in Crown units to fight for Britain, though Britain had hoped initially that many more would take up arms. Britain captured virtually every major city during the course of the war and loyalist activities played a critical role in many British victories.
State-sponsored persecution of loyalists denied them civil liberties, seized their properties and ruined their livelihoods. This, along with Patriot mob violence left thousands of loyalists with little choice but to leave America. Most were not rich, but poorer, blue-collar labourers, artisans, farmers or tradespeople who had lost everything.
It's estimated that 60,000 to up to 80,000 loyalists migrated to other colonies in the Empire or back to England. While some did return to America, a majority -- 35 to 40,000 -- found their way to the Maritime colonies in Canada, primarily to nearby Nova Scotia, while others went to what is now Ontario and Quebec. Some would later return to the U.S., but most did remain in Canada. This migration would have a profound effect on the development of an English Canadian identity in the years to follow.
This total didn't include the indigenous peoples who sided with Britain, in an effort to stave off American westward expansion into the Ohio Valley (which was deemed Indian Territory since 1763). Nor did this include the thousands of Black Loyalists (up to 20,000) who took up arms for Britain in exchange for their freedom from slavery.
Natives and blacks who fought for the Crown were offered land grants in Canada and in other colonies and/or monetary compensation, but these tended to be inferior to those given to white loyalists and they often faced discrimination, economic hardship and harassment. Some blacks found it untenable to remain in Canada and moved to the free colony in Sierra Leone.
Britain and the natives still relied on each other for military/political/commercial interests in the interwar years, though it was often an uneasy and fractious relationship. Natives would continue to maintain alliances with Britain for political or commercial reasons until the end of the War of 1812, when Britain abandoned their interests at the peace negotiations.
More can always be said on this, but this panel from our 2020 Conference might be of interest , specifically the paper from /u/irishpatobie, as well as his discussion in the AMA thread, as it deals with post-war Loyalists.