The policy of appeasement pursued by the Chamberlain government was designed to prevent the outbreak of another World War. The First World War was still fresh in most people's memories, and there was no appetite to fight another one.
That being the case, the Chamberlain government pursued a policy that satisfied some of Hitler's territorial demands in Europe, most notably the predominantly German-speaking territory of the Sudetenland in Czechoslovakia. Chamberlain, along with the French Prime Minister Daladier, signed an agreement at the infamous Munich Conference in 1938, the high watermark of appeasement, which allowed the Germans to occupy the Sudetenland.
When Chamberlain returned home to Britain, he was given a hero's welcome. Triumphantly declaring that he had achieved "Peace in our time," he believed, as did most of his relieved fellow countrymen, that a Second World War had been averted. It soon became clear that this was not the case.
In 1939, just one year after signing the Munich Agreement, Hitler invaded the rest of Czechoslovakia. The Nazi leader had said that the Sudetenland would be his last territorial demand, but that was a total lie.
Unfortunately, Chamberlain had fallen for that lie, and in the wake of the German invasion of Czechoslovakia, it became patently obvious that the whole policy of appeasement had been built on that lie and was predicated on the spurious notion that Hitler could be trusted.
In the event, appeasement was a total failure. It didn't prevent the outbreak of a Second World War, as Hitler was always determined to carve out a racial empire in Europe by armed conquest. That being the case, no amount of appeasement would ever have been enough; Hitler would've just kept on upping the ante and making ever more outrageous territorial demands.
As well as being disastrous for the stability of Europe, the policy of appeasement didn't even achieve its immediate goal of keeping Britain safe. On the contrary, appeasing Hitler had allowed the Germans to become militarily stronger, which would in due course allow them to threaten Britain directly.