The German expansion into Austria helps to set the stage for future designs of Hitler and the Nazi party. The pattern that would be visited repeatedly was first established in the overtaking of Austria. On one hand, Hitler laid out a type of "historical" case as to why expansion was warranted. This perception of history was distorted, but since no other versions were being offered (or those who were offering it were being silenced by Hitler), there became a historical basis for the land acquisition. Some slight attempts at diplomacy was pursued, consisting of Hitler meeting with representatives and essentially bullying his way to his own ends, and then a military movement complete with social modes of control that emphasize the Nazi notion of the good being absolute. All of these were on display with the acquisition of Austria. If you believe MGM musicals, the Von Trapp family had much to say, or sing, about this, as well.
To me, the main significance of this event is that it marks the first real attempt by Nazi Germany to expand its borders. This expansion would lead to the start of WWII.
After Germany took over Austria, it went on to demand part and then all of Czechoslovakia. After that, it thought it could take Poland with impunity. It was this invasion that led to the war.
The actual annexation of Austria had little impact outside of Austria. I think its only real importance is that it was the start of a series of moves that led to war.
The first result was some very unhappy Austrians. Germany had been trying over a period of four years to get hold of Austria and make it part of Germany. Hitler decided to bully Chancellor Kurt von Schuschnigg into an allegiance. Hitler and his troops marched into the country following Schuschnigg's resignation and took charge.
Hitler was very proud. It meant the return of "German-Austria to the Greater German Reich." There were many Austrians in favor of the allegiance and annexation. Soon after the anti-semantic movement took hold, Austrian Jews became the target of wide spread abuse and deportation. The take over ceased to make Austria a neutral player and pulled their allegiance into the war causing men to be enlisted in the dream of the Third Reich.