Appeasement was the approach that European leaders took towards Hitler's aggression in terms of land acquisition. Hitler's desire was to reappropriate lands that did not fall under the defined boundaries of Germany as dictated by the Treaty of Versailles. Western European leaders such as Neville Chamberlain of Britain felt that "appeasing" Hitler's demands to increased land acquisition could avert the prospect of another prolonged war. The fear of World War I and the hope of "peace in our time" helped to motivate the policy of appeasement. Too much of a gentleman to recognize that Hitler wasn't, Chamberlain's policy was manipulated by Hitler to overtake more land until a large majority of Europe was under Nazi control. Appeasement is seen as a failed approach in large part because it ended up giving into to Hitler as opposed to stopping him.
To "appease" someone is to give in to their demands in hopes of avoiding further and greater demands and/or in order to avoid having to fight them. This is what was involved in the policy of appeasement that was taken by Britain and France before the start of WWII.
Hitler was very unhappy with the Treaty of Versailles and he wanted to do various things that would violate that treaty. These involved things like rearming Germany and taking territory that Hitler felt should be German. The policy of appeasement consisted of allowing him to do these things in hopes that he would not do anything worse.
For example, then, when Hitler wanted to take the part of Czechoslovakia known as the Sudetenland (because ethnic Germans lived there) the French and British allowed him to do so. They did this in hopes that that would satisfy him and a war could be avoided.
–It was the policy followed by leaders of Britain and France at the 1938 conference in Munich. Their purpose was to avoid war, but they allowed Germany to take the Sudetenland from Czechslovakia.