Appeasement is basically when a nation or government turns a blind eye to enemy activity for diplomatic or political reasons, usually to avoid conflict or escalation of the situation.
When Germany began military aggression against neighbouring countries, most of the world's powers turned a blind eye to the situation, even though they didn't agree with Hitler's policy - they made the decision not to intervene, in the hope that war with Germany could be avoided.
As we all know now, that didn't last very long.
Appeasement of brutal regimes and dictatorships carries on to this day, with the conflict in Syria being a good example.
Many believe the Syrian dictator responsible for the current conflict has been able to manipulate the West's lack of appetite for further military combat in the Middle East in order to broker a form of appeasement, despite his brutal policy of genocide and torture being widely condemned.