History is important because WE ARE the past: we are the sum of all the events--good, bad, and indifferent--that have happened to us. This sum product guides our actions in the present.
This is true not only for the individual (imagine what would have happened to you had your parents never met, or had your parents raised you with different values), but for large societies as well (how would the U.S. be different, for example, if it had lost the American Revolution, or if the Spanish had founded the colonies of North America that became the United States?). In both cases the United States as we know it would not exist.
The only way we can understand who we are and how we got to be that way is by studying the past. Similarly, the only way we can understand others is by studying their past. If we don't understand what made them who they are--in terms of how they think and act--we will make all sorts of mistakes in our interactions with them. Think of how you treat people differently based on how you know them. The same is true for countries when it comes to diplomacy. Our failures in Iraq were borne of a limited understanding of who they are (because we haven't taken the time to truly study and understand their past).
"We study the past to understand the present; we understand the present to guide the future." -- William Lund