Welcome to PF;
... what is the context for the question? It seems somewhat philosophical: what is beauty?
The short answer is that there are no hard and fast definitions to work from. To a large extent we know these things when we see them but when we try to nail them down rigorously we run into exceptions... like with a fractal.
Look: stars are pretty ... some people just leave it at that, some want to know more.
If you are someone with that kind of curiosity, you will tend towards science anyway.
It is important because we are interested in it. I could fill you in with historical importance: with political influence held by wrong ideas, or how improving our understanding of the World in general improved life for the greatest number in the long run, but it boils down to being important because we are interested in it ... and we are interested because we have evolved as curious apes.
What made you interested in astrophysics/astronomy? Why is it beautiful? Why is it important?
The thing that made me interested in astrophysics/astronomy was the big bang theory. It is beautiful because just look at those HST pictures! It is important because there are many dangers that can come from space, and finding ET too.
Well you ask good questions.
As for me astronomy is so interesting job. When you look some pictures from Hubble you understand all powerful and wonderful of space.
I think anyone want to know "Are we alone?" "What was before big bang?" and other. I hope people who work in astronomy and astrophysics can find answers to the questions. And people who work in NASA are lucky.
Astronomy have been opening to us beautiful universe and we are part of this.