Being a student of history myself, I possess a slightly biased view. I think that the frame of reference in understanding our past setting is a powerful element in comprehending our current one. This is not to say that everything is repetitive, but that past history contains some relevant connections to today's setting. For example, in attempting to fully grasp the implications of the BP oil spill in the Gulf, one need only look back on the Exxon Valdez situation in the late 1980s to find some scope of environmental or economic impact. In our current battle against terrorism and government's role in it, understanding other moments where the political order has appropriated a mistrust of "the other" can help to shed some light on the situation. Finally, examining previous periods of economic constriction might help to give some level of understanding as to how the current economic crisis might resolve itself.
Events tend to occur in patterns where humans are involved. History is the record of those patterns. By studying the history, then, we are able, often times, to accurately predict what will happen in the future, or recognize what is happening in the present because we can see the pattern taking shape.
The "layers" of historical evidence add up over time, and give us a clearer picture. As I tell my students at the beginning of each school year, "everything had to happen exactly right for you to walk through my classroom door today". We are the collected result of all the history that has gone before us.
Ideally, the lessons of our history help us understand what is going on in the world today and help us to cope with the problems that we encounter. For example, we can hope that history will tell us how to deal with problems that seem to recur. We might hope that we would learn how to deal with insurgencies in countries like Iraq because we have seen many countries try to deal with insurgencies like that.
The problem is that history is not clear -- it does not teach us unambigious lessons. Instead, every situation is a little different from those in past times. In addition, there are many possible historical lessons to be learned. Because of these problems, it is much harder for us to learn from history than it seems like it should be.
The question appears rather confusing. The difference between "history" and "understanding history" mentioned in the question is not clear. So I will discuss here how history or study of history help us.
History is the study of the human past, covering aspects such as social, cultural, political, and economic conditions and economic. While some people may study the past simply to understand how people of other times acted and thought. However, all people can benefit from understanding of history by drawing lessons from past actions and thoughts as a guide for decisions and policies today. Thus by studying history we can avoid making mistakes made by others in the past.
History also helps us to trace past root of people and practices. This helps us in understanding the present better. For example the culture and characteristics of people in different societies is influenced by their past. In this way history helps us to understand the people and culture better and react appropriately to them. For example, people who lived through the hardships of the great depression of 1930's developed an attitude of frugality that is totally alien to the generations that did not experience the great depression. An understanding of history of great depression is likely to make these people more understanding towards feelings of people who have gone through such hardships.
The past refers to the actual incidents that have already taken place. History in addition to recording the factual details of the past offers to analyze the causes and results of the past incidents and thus offers explanations and interpretations of these past incidents. Hence the study of history proves invaluable in tracing connections between what took place in the past and what is happening in the contemporary present.
For example the parallels between the present economic crisis and the Great Depression of the thirties have been analyzed and widely commented upon in great detail by economists all over the world.
The reason why the past is studied in great detail in relation to the contemporary present is mainly to avoid the mistakes of the past.