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The phrase neutron rich, meaning "with a lot of neutrons", is commonly used in relation to several phenomena within astrophysics. An isotope can be described as neutron rich if it has more neutrons than typical for the element. i.e., if it is toward the "upper" edge or beyond the valley of beta stability. (The opposite is neutron poor aka proton rich.) Such isotopes can result from the r-process, and undoubtedly occur to some small extent during other kinds of nucleosynthesis. Neutron stars can have layers in which neutron rich isotopes that would ordinarily be unstable, but exist due to the high pressure. Underneath these layers they have neutron degenerate matter, which can be described as neutron rich.
Material in which the r-process is presumed to occur (e.g., gas-like material within or ejected from explosions such as supernovae or compact object mergers) is described as neutron rich, meaning the material includes many free neutrons. Free neutrons decay into protons in minutes, placing limits on how much the r-process can occur.