Germany invaded Poland on September 1, 1939. Since Great Britain had pledged military support to Poland if it were attacked by the Germans, it subsequently declared war against Germany on September 3, 1939, hence beginning World War II.
Great Britain had suffered terribly in World War I. As Great Britain and France were keen to do everything possible to avoid a repeat of that conflict, they made an attempt to appease Hitler by allowing aggression against Austria and Czechoslovakia to go unchecked. By the time Germany had begun to mobilize against Poland, it had already successfully taken over both of those nations.
Hitler had much more conquering in mind and his plans for additional land acquisition was not known by the rest of the world. When Hitler signed a pact with Soviet leader Joseph Stalin in August 1939, Great Britain was immensely concerned. The pact with the Soviets placed Germany in a position where a war with Poland could be fought on a single front. The German attack on Poland was carried out in rapid fashion and included heavy air bombardments as well as armored land divisions. Polish defense forces were no match, and Great Britain and France felt compelled to come to their aid. World War II had begun.