What it is: To appease people is to try to calm them by doing what they demand. In politics, appeasement means agreeing to at least some of the demands of a potentially hostile group or state, in the hope of preserving peace.
What it means: The word is particularly associated with events before the Second World War. Neville Chamberlain, British Prime Minister from 1937 to 1940, wanted to prevent war with Germany. In 1938 he had a series of conferences in Munich with Adolf Hitler, the German dictator. Chamberlain agreed that Czechoslovakia could be divided up and the German-speaking border areas (Sudetenland) taken over by Germany. He believed that this concession (however tough on the Czechs) would stop Hitler from going to war. Appeasement is not the same as pacifism; pacifists might look for other responses - such as nonviolent resistance - to a dictator's aggressive demands.
Think about it: Probably everyone has tried out appeasement in some way or other: 'anything for a quiet life.' Some people think appeasement is 'giving in', a humiliation. But for many others it simply means letting someone have their own way about something that may not be all that important. Keeping assertive people sweet seems a sensible aim. But appeasement is tricky, in the extent of power it allows other people to have. One has to think about what they are really asking for, and whether it could cause harm if they got it. So, where to draw the line while still keeping the peace? Not only 'where': how? (And if you are the one making demands, can you persuade yourself to see another point of view? Or do you want to keep the upper hand no matter what?)