Appease means to make or preserve peace with a nation, group, or person by giving in to their demands, or to relieve a problem, as in "the cold drink appeased his thirst."
The word often implies abandoning your moral principles to satisfy the demands of someone who is greedy for power: Think of British Prime Minister Chamberlain's attempt to appease the Nazis at Munich. The cold drink appeased his thirst. Appease is from Middle English apaisen, from apaisier, formed from the prefix a- "to" plus pais "peace," from Latin pax.