To make peaceful and quiet; to calm, satisfy.
The Aztecs offered mass human sacrifices -- of 80,000 prisoners on one occasion! -- in order to appease their gods.
When the European nations agreed to let Adolf Hitler take over part of Czechoslovakia in 1938, in a vain attempt to prevent a larger war, their opponents shouted that they were practicing a foolish appeasement that was doomed to fail. (They were right -- within months Hitler had violated the pact.) A child's anger may be appeased with a little effort; an angry god or goddess may demand something extreme. We may speak of hunger being appeased by food. Appeasing usually involves giving something, whereas pacifying can refer to anything from stroking a baby to using armed force to stop an uprising.