Do you observe the sky with telescopes? No. That is the work of my friends the astronomers. I work with particle accelerators.
Do you build nuclear weapons? No. The type of nuclear physics research I do is safe for you.
Is there extraterrestrial life out there? I hope so.
Do you work with the Large Hadron Collider at CERN? No. Most of the nucleosynthesis processes in stars occur at relatively low temperatures for LHC standards. Smaller low energy accelerators are better suited for my kind of research.
Are you a doctor? Yes, but I don't have a stethoscope.
I thought we already understand the origin of the elements. Why do you work on something we already know? We know stellar interiors forge most of the elements. The precise mechanism(s) for making each nuclear species is very uncertain in best case scenarios. It is completely unknown in the vast majority.
I thought God made everything around us. Why do you waste your time? We nuclear astrophysicists have not had the need to make reference to God in our theories. So far we have been able to do work supported by other principles. Our predictive power is quite good, though.
Why should I care about nucleosynthesis and stars? How does it affect my life? Because you are made of starstuff.
What are the most important open questions of nuclear astrophysics? At random, I'd say:
0) The solar neutrino problem Done
1) The astrophysical site of the r process
2) The fusion reaction rate of 12C+12C
3) The Equation of State of matter at nuclear densities.
4) The energy spectrum of neutrinos in core collapse supernovae
5) The thermonuclear rate of alpha + 15O
6) The mechanism of mass loss in massive stars
7) The mechanism of radiative transfer in stellar atmospheres
8) The thermonuclear reaction rate of 12C + alpha
9) The mechanisms of convection, semiconvection, and mixing in stars
10) The Li problem
11) The funding and construction of FRIB