There were two main reasons for this.
First, by the 1930s (which is when appeasement really began) the European countries felt at least somewhat guilty about their treatment of Germany in the Treaty of Versailles. They felt some of the terms might have been unjustified and that the Germans might have some just cause for violating them. These attitudes were magnified by Nazi propaganda about things like the need to protect ethnic Germans in Czechoslovakia.
Second, and more importantly, the European countries were not prepared for war and had no desire for war. The memories of World War I were very fresh at this point. There was no desire for another big war that might be similar to that war. The Europeans had reduced the sizes of their militaries and were not sure that they would be able to defeat Germany easily. They overestimated German strength early on when they actually could have defeated Germany easily. Since they thought that standing up to Germany would provoke a war they did not want, were not ready for, and could well lose, the Europeans chose to appease Germany and hope that no war would be necessary.