I've loved studying history for as long as I can remember, and if I could I would enjoy majoring in history in college someday with the hopes of a career in it.
At the end of the day, I know history is important - studying it, being aware of it, discussing it, etc. But when I asked myself why is it important, I realized I didn't have an eloquent answer prepared, and I wouldn't know what to tell someone if they asked me beyond a one line answer of "Well, it teaches us about where we came from and how we got there and where we're going."
I know I study it because I'm passionate about it, because I delight in learning how people lived hundreds of years ago, what society was like, and how we got here.
But beyond that, or to elaborate on that, why is it important that, perhaps, at least the general population has a base knowledge of history, if not why it's important for specialized historians (and any job that relates to history) to exist?
It's a lot like asking "why is anything in the humanities important". It's true our world, our technology, can exist and function without art, music, history, etc, but then it would be a bland, boring, arguably meaningless existence.
The humanities, history included, is a study on the human experience, that very thing that sets us apart from machines and animals; it's our penchant for curiosity, individuality and our desire to understand what it means to be human. Maybe a historian specializing in early Germanic belt-buckles won't produce a tangible effect on the course of human history in his or her lifetime, but the mere pursuit of that knowledge gives us a glimpse into how humans thought, how they defined meaning. Belt buckles, crusty old Roman sandals and even early 20th century bottle caps are human products, and if we care about ourselves, then we should just as well care about what other humans of all eras of human history wrote, produced, what they ate, what they did, how they fought, and how they loved.
In short, history, like art and music, is a culturally enriching pursuit. We need it to understand our nature, and to advance as a species. Human development is proportional to how much history we've recorded and deciphered.
For me, the study of history, both professionally and as a passion, has always given me perspective. It provides context for why our current times are as they are. It helps me to put things in perspective and make up my mind about developments. And, as history doesn't repeat itself unless it does, it can also provide insight in how things might turn out in the near future.
It might sound grand and a bit pretentious, but without knowing about history, figuring out your place in it simply is a lot more difficult.