Short answers, pulled from the story.
Appeasement was a diplomatic policy of making political, material, or territorial concessions to an aggressive power with the intention of avoiding conflict. It is most closely associated with the British foreign policy between 1935 and 1939 under Prime Ministers Ramsay MacDonald, Stanley Baldwin, and above all Neville Chamberlain toward Nazi Germany.
The Munich Agreement was signed on the 30th of September 1938 by Germany, the United Kingdom, France, and Italy. It required Czechoslovakia to cede the Sudetenland to Germany. On his return to Britain, Chamberlain delivered his famous "peace for our time" speech to crowds outside 10 Downing Street, and the royal family invited him onto the Buckingham Palace balcony before he had reported to Parliament.
Multiple pressures converged: anti-war sentiment following World War I, belief that the Versailles Treaty had been unjust to Germany, anti-communism among the conservative elite, and military assessments that Britain was not ready to fight. The Royal Air Force warned in October 1938 that German bombers would likely get through for at least the next twelve months, since Hurricanes and Spitfires were not yet operational at scale.
The Labour Party opposed the Munich Agreement, and a small number of Conservative dissenters also refused to support it. Winston Churchill warned the week before Munich that the partition of Czechoslovakia under British and French pressure amounted to complete surrender to Nazi force. Secretary of State for War Duff Cooper was the only Member of Parliament to advocate war and resigned from the government to protest the agreement.
Guilty Men, published by three British journalists writing under the name "Cato", called for the removal from office of 15 public figures it held responsible for appeasement, including Chamberlain. The book defined appeasement as "the deliberate surrender of small nations in the face of Hitler's blatant bullying". It is said to have contributed to the Conservative Party's defeat in the 1945 general election and shaped subsequent thinking about the policy for decades.
Historians have moved through several phases. A.J.P. Taylor's 1961 book The Origins of the Second World War argued appeasement was a rational, active policy by men confronting real problems. Counter-revisionist historians in the early 1990s, including Frank McDonough, concluded it was probably the only option available but was poorly implemented and came too late. McDonough's view is sometimes called a "post revisionist" position, arguing that Chamberlain's worst error was believing he could lead Hitler toward peace.