I find it really interesting. We know very little about how gravity works. To try and understand it we investigate places that have really strong gravity. Much stronger then the gravity we experience here on earth. We are interested in strong gravity as this is a great way of testing our current knowledge of physics in extreme environments. By doing this we should be able to learn more and build on our current ideas.
Neutron stars are the second most compact objects in our universe, after black holes. The gravitational pull created by a neutron star is incredibly strong. Neutron stars are great to study because we can see them, and see how they evolve over time.