I note that you have tagged this with "Holocaust" so I will answer with regard to this particular historical tragedy.
The Holocaust has shaped the world we live in today to a great extent. Because of it, we are much more worried about human rights than we probably would have been without the Holocaust. We say we are determined to ensure that no genocide will ever happen again. We have not been perfect on this score, but we certainly try harder than we used to.
In addition, the Holocaust caused the creation of the State of Israel. The existence of this country has shaped the world we live in. It has done so much to define the relations between various countries in the Middle East and between the US and those countries.
The shadow of historical tragedies like the Holocaust affects the way we act and the world we live in because we are determined to make up for them and to prevent them from reoccurring.