Do you think that jury duty is an important civic duty, or do you think it's a burden?

It is a matter of opinion, I suppose. 
We need jurors, of course, but with so many people who hate it, there surely wouldn't be enough if the goverment simply allowed whoever wanted to volunteer to be the jury. I suppose that makes it sound like a burden, as it's a goverment-ordered requirement, like taxes. It is a privilege, though, if you think about it. Being selected for jury-duty means that you're a reliable citizen of America and you're trusted enough to help make a very important decision. 
So, to restate my initial response, Jury duty can be seen as a duty or a burden, depending on how one views it.

Jury duty is an important civil duty because it lets citizens be involved in the judicial system. Instead of just giving your opinion after the verdict citizens get to play a role in deciding a verdict.