1: Germany's opposition to the Treaty of Versaille
The Versailles Treaty, which followed WW1, was rather very harsh on Germany. This provoked the seeking of revenge within Germans; they were very angry about the way they had been treated with regards to the First World War (were expected to take all the blame and pay £6600million in reparations). Also, Hitler's hatred towards the Treaty/League of Nations made him increasingly (and worringly) popular in Germany at the time - he used his opposition to the Treaty/League as an advantage for his campaign to get elected etc.
2: The failure of the League of Nations
By the 1930s, the League of Nations was a weak organisation. It did not achieve its original aims: prevent aggression, encourage cooperation, work towards disarmament...all to prevent a war. It had failed to deal with the challenges it faced (these include the Manchurian/Abyssinian crises). Meanwhile, in Germany, Hitler sat back and watched how powerless the League really was. This encouraged him to go against the League even more as he felt nothing would happen to him if he did so. Plus, the League was not very fair to Germany after WW1 - by means of the Treaty of Versailles, not inviting them to peace conferences etc. We get the impression that if they had been treated more fairly, then they would not have wanted revenge (a war) so much.
The policy of appeasement essentially involved giving Hitler what he wanted, in the hope that he would not demand for 'as much' and become more friendly rather than aggressive. However, it did not go exactly as planned - Hitler was able to expand his territory and become stronger by way of asking Britain and France for more and more. He grew more confident and his aggression furthered. Appeasement delayed the war; it meant that it would be more serious when it finally did break out. It did not cause the war as such.
4: Hitler's Actions
Through appeasement, Hitler was able to build up his armed forces throughout the 1930s. This was part of Hitler's Foreign Policy; to abolish the Treaty of Versailles. Adding to rearmament, he also united with Austria (Anschluss) and took over many parts of Europe. His unlimited demands would have caused a war in the end anyway. His aggression provoked a war too. Germany's invasion of Poland, though, was in fact what triggered the Second World War. Hitler pushed his luck and did not think Britain/France would do anything if he invaded Poland - as they did not do anything when he did other things! However, he was wrong - Britain and France felt it was time to deal with Hitler...the day after he invaded; they declared war on Germany and WW2 began.
Other factors to consider...
The Depression: Leading members of the League (e.g. Britain, France) were too focused on solving impacts of the Depression within their own countries to worry about dealing with the League's issues/international concerns/Hitler.
The Manchurian & Abyssinian Crises: Hitler saw how the League did not act when Japan invaded Manchuria, and when Italy invaded Abyssinis. This encouraged him to think they would not do anything if/when he was to do something like that (i.e. invade Poland).
The USA/USSR were not League members: These two major powers could've helped out several of the League's challenges, yet they were not members. Without them, the league was considerably weak and Hitler became even more ambitious. Hitler/Germany would've also been weaker seeing as the USA/USSR would not trade or lend loans if they were part of the League of Nations.