I often tell my students the best way to understand history is to understand Newton's second law: For every action, there is an equal opposite reaction. Precious few events in history have occurred in a vacuum. The large majority were directly related to and in response to previous events. There was a movement several years ago to teach history backward, beginning with the present and how it connected to events in the past. I firmly opposed this approach; but its one redeeming attribute is it does allow students to see the connection between the past and present. To cite an example: if one examines race relations in this country, one is soon led to the civil rights movement. From there, one is led to the Black Codes of Reconstruction and from there to the slavery era. Slavery itself can be traced to the age of exploration and also the development of an attitude of superiority among people of Aryan heritage. That can be traced to the Aryans' development of metal weapons and the use of horses which made them a fierce fighting force on the Indo-European plains and a belief that they were superior to those they conquered. There are a lot of holes in this thinking, obviously, but the lineage and connection should be clear.
"History" is a record of events that happened in the past. History may be personal and recent (what did you do at school yesterday?) or inclusive and based on long ago (how did humans spread throughout different locations around the world?) or anything in between those two extremes.
History is a link between the past and the present because people act now, in the present, based on lessons learned in the past, from history. You may have had a frightening experience with a strange dog at some point in your past, and as a result you may still be afraid of dogs. Humans discovered that fire was warm and felt good when it was cold, but learned that fire could hurt them and could destroy objects. The decisions individuals and groups make in the present reflect knowledge gained through history.
The idea in this statement is that in order to fully understand the conditions of the future, one has to look to the past. The statement asserts that there is a great deal of connection and relevance between what exists in the past and what lies in the future. The belief is that there is an inextricable link between both. This might lie in the realm of lessons learned, morals that guide the way one acts, as how past events can serve to foreshadow what lies in the future. The statement is not necessarily saying that the past causes the future, but rather that in understanding he past, one can better help to understand the present and the future. The idea here is that there is not a way to fully divorce ourselves in the present and future from what has happened. As human beings, the quote indicates that we are bound to it and must recognize how the past plays a role in understanding where we are and where we will be. History, thus, is a study of human behavior both in the past and in the present and future.