A "jury" is a group of normal citizens who decide a court case.

If you live in a country that has a jury-based legal system, you may have to serve "jury duty". This means that you are responsible for being on a jury and deciding a legal case:

I just found out that I have jury duty in two weeks.

In countries where jury duty is required, a lot of people find it inconvenient and boring. So it's common for citizens to try to avoid jury duty by making the judge and lawyers think that they won't be able to make a fair decision.