What is appeasement policy? Who was appeasing who leading up WWII?

Appeasement policy is using diplomacy to try to avoid a war. It means looking at the situation from the other party's point of view and trying to fix whatever grievance or sore point might lead one's opponent to warfare and destruction. The rationale is: if we simply give the other side what it wants, it will be contented, the problem will be solved, and we can all move on.
Appeasement is most closely associated with the actions of British Prime Minister Chamberlain in the late 1930s as tensions with Germany were building towards another world war. Countries like England and France had suffered greatly in World War I. The death toll had been very high, and Britain, in particular, had exhausted its finances fighting that war. There was worry that the public would rebel against another major war. With one traumatic war only twenty years in the past, Chamberlain feared the effects of another.
Chamberlain wrongly thought that handing an ally, Czechoslovakia, over to Hitler (which was what giving him the Sudetenland effectively did) in 1938 would finally appease Hitler's appetite for territory and avert a war. It is one of the great bloopers of history and surprised even Hitler himself. Obviously, it didn't work.