Why is the fact that the president gets to nominate new supreme court justices important?

Because the supreme court has a lot of power. Their rulings can set government policies, can nullify laws. In addition supreme court justices are nominated for life, so they keep this powers for years, possible decades. This power is derived from the deliberate vagueness of the Constitution (example: what is torture? is the right of the mother to protect her body higher than the right to life of the unborn child?) The Court of Justice plays a major role in abortion, single sex marriage and other high profile situations. At this moment the majority of the judges are nominated by republic presidents (conservatives?), if Obama nominates more liberal judges this can actually result in a major change in the American society.