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.