The notion of appeasement was something that the leaders of France and Britain pursued in the hopes of quelling the mounting crisis. The belief of leaders like Neville Chamberlain of Britain was that the effects of World War I were so horrific in nature that they needed to be avoided at all costs. The theory of appeasement suggested that if Hitler's demands were met without resistance, but with assurance that bloodshed could be avoided, then war could be avoided. Too much of a gentleman to understand that Hitler was not, in the words of Clive James, appeasement ended up giving Hitler more power through territory. Hitler continually made promises to leaders like Chamberlain and continually broke them. This made him too powerful to confront, and in the process, emboldened the Nazis and their leader. Appeasement, though rooted in a very conflict preventive approach, ended up causing more damage.
Agreed with the above post. They buried their heads in the sand and hoped Hitler would go away, mostly. Then they ignored him furhter when he did not, and at their own peril. However, France did build a large military and an expensive, massive fortification called the Maginot Line that they believed would be impossible to breach. Hitler just "blitzkrieg-ed" around it by going through Belgium.
They also formed an alliance with one another, and wth the Soviet Union. They even practiced brinksmanship - a foreign policy where they threaten war if a certain action is taken, gambling that he will not. They did this after Czechoslovakia was taken, and threatened Hitler with war if he invaded Poland. It's a way of trying to prevent war by threatening war. It worked about as well as appeasement did.
Basically, what the British and French tried to do to prevent war with Germany is something that is called "appeasement." What that means is that they tried to give in to German demands in hopes that there would not be war.
What Britain and France did was to pretty much let Germany do what it wanted -- the let it unite with Austria, let it take the Sudetenland, let it take Czechoslovakia. They basically told Hitler "okay -- take that, but don't take anything more."
Obviously, it didn't work and they declared war when Germany invaded Poland.