Science question: why do hydrogen and hydrogen compounds such as water make good neutron shields? Does the hydrogen absorb the neutrons? What goes on there?
Particle interactions are governed by their respective cross-sections.
Think of a target. If its cross-section is larger, you stand a higher chance of hitting it. So it is with particles, that the odds of an interaction increase in certain circumstances.
As conditions change, the cross-sections change as well. So what works for capturing slow neutrons (also called thermal neutrons, because their average kinetic energy comes from their thermal motion, governed by temperature) might not work for capturing fast neutrons.
Hydrogen 1 has a decent enough cross-section for capturing neutrons that any substance with a lot of hydrogen that can stand the heat is a decent and cheap shield. That being said, there are better materials to use:
https://en.wikipedia.org/wiki/Neutron_cross_section#Typical_cross_sections
Notice that the table gives cross-sections for scattering, capture and fission. Also notice how wildly the number differs between thermal and fast neutrons.
So while you can use stuff like Gold or Cobolt, it's cheap and easy to use water.
Notice that Hydrogen is stuck in the "Moderators" category. That's because its cross-section for scattering neutrons is higher than for capture. It can therefore decrease neutron energy by taking some of the kinetic energy during an interaction. So it's a good thing if you're trying to slow neutrons down.
Thermal neutrons are easier to capture and trigger nuclear reactions more easily. Check the capture cross-sections of neutrons for U-238 and for U-235 for fast neutrons, then for thermal neutrons. Notice that for fast neutrons it's:
1.) Difficult to capture them
2.) The cross-section is about the same for U-238 and for U-235
U-238 will capture a neutron without fission, turning into U-239, but U-235 will cause fission. So U-238 is kind of a sink of neutrons. But if you slow them down into thermal neutrons, U-235 becomes ~50 times more likely to capture neutrons than U-238, so fission can continue without a giant loss of neutrons.