History is like a tree—the ancient parts are roots, and as the story progresses the trunk rises and branches expand to encompass every person and event since Adam and Eve. Because history is unified, every element of the story is interconnected, even if that connection is distant. Furthermore, the current parts are all directly the product of the parts that have come before, and to understand the current situation you'll need to understand the past.
Understanding the ancient history roots at the bottom of the tree is essential for a proper perspective of everything that comes after. Some people take this too far and assume that ancient history is all that matters, but those who disregard it or understand it on no more than a cursory level are just as mistaken. Just as a building must have a strong foundation, so a study of history must begin in the right place.
The ancient world was different from ours, and the same. It was different in primarily physical ways: technology was less advanced, there were fewer people, and the general standard of living was far below what we enjoy (at least in the industrialized world). However, human nature never changes, and the same universal conflict that exists today—between God's children and His enemies—raged then.
It's interesting to what extent the dominant theories and philosophies of the modern world reflect those of the ancients. There is truly nothing new under the sun, and the Enlightenment rationalism, faith in human progress, belief in man's innate goodness, evolutionary idealism, and even postmodernism against which Christians fight all have their roots in the ideas of the Babylonians, Greeks, Egyptians, and every other early civilization.
That doesn't mean there isn't a clear trajectory from the ancient world to the present. Ideas all run a distinct course, and some reach prominence at different times; while the seeds of every successive philosophy were sown in the ancient world, it took time to grow them into what we recognize how as humanism, modernism, postmodernism, and the ever-illusory post-postmodernism.
The same is true of events. The history of any period is simpy the chronicle of man's attempts to thwart God's will and Yahweh's use of even the most outrageous rebellion to achieve His own ends. In some ways, this is more obvious in ancient history, as the nation of Israel fought the surrounding nations, and too often embraced their paganism.
That story, of God's work among His people and in the world, and of man's continual rebellion, is also our story. The Church fights the same battles our Israelite forefathers did, though on a more ideological rather than physical scale. When we realize how much the story of the ancients is our own story, the significance of studying their world becomes much clearer, and the urgency of such study is made plain.