Astronomers often believe that the significance of their work is self-evident. But in these harsh times, even the most obvious benefits of an activity come under scrutiny. It all depends on your perspective and circumstances in life. If you are poor and struggling to get by, there is virtually no activity by other people that is justifiable unless it results in direct monetary gain by you. If you are wealthy, virtually any activity can be justified so long as it either has no effect upon you, or provides some enhancement to your life either culturally or materially.
Astronomy is important to some people's lives because it lets us experience a larger reality beyond the 9 to 5 workday, or the limited horizon provided by living on this one small planet in an incomprehensively vaster universe. Many of us find great beauty in exploring this arena, and the tantalizing glimpses it gives us to how our planet, solar system and universe have evolved over billions of years.
There are also a few pragmatic reasons why we must continue to study the universe. The Sun affects climate on the Earth, but there is much about the Sun that we do not know. Only by studying other stars can we better understand how the Sun changes over time. Also, buy studying the motions of objects in our solar system, we can keep track of objects that may one day impact the Earth, which may cause lethal climatic changes.