The Department's fairly detailed discussion is here. An excerpt:
[Previous] regulations generally prohibited visitors from possessing an operable and loaded firearm in areas administered by [the National Park Service and the Fish and Wildlife Service] unless the firearm is used for lawful hunting activities, target practice in areas designated by special regulations, or other purposes related to the administration of federal lands in Alaska....
[T]he Department's final rule amends the regulations to allow individuals to carry concealed, loaded, and operable firearms in federal park units and refuges to the extent that they could lawfully do so under non-conflicting state law.... [T]o the extent that a state's law recognizes licenses issued by other States, including the applicability of reciprocity agreements, the final rule would similarly recognize such reciprocal authorities.
There are FAQ's here. Some excerpts from that:
Q: Won’t visitors and wildlife be endangered by allowing concealed firearms in parks and refuges?
A: No. The final rule continues to maintain existing regulatory provisions that prohibit poaching, unauthorized target shooting, and other illegal use of firearms. Additionally, individuals authorized to carry firearms in a park or refuge will continue to be subject to all other applicable state and federal laws. We have no reason to believe that law-abiding citizens who carry concealed firearms will disregard these prohibitions and use their firearms for illegal purposes. Moreover, the final rule does not affect existing rules limiting the possession of loaded rifles or shotguns.
Q: Aren’t parks and refuges already safe places? If so, why allow people to carry concealed firearms?
A: America’s national parks and refuges are often safe places to visit, and our law enforcement officials are working to the best of their abilities and resources to maintain visitor safety. However, we also recognize that current statistics show an alarming increase in criminal activity on federal lands managed by the Department of the Interior, especially in areas close to the border and in lands that are not readily accessible by law enforcement authorities. In these circumstances, we do not believe it is appropriate to refuse to recognize state laws simply because a person enters the boundaries of a national park or wildlife refuge, or because there is a lesser chance that a visitor will be harmed or potentially killed by a criminal in a national park unit or wildlife refuge.
Thanks to John Hollingshead for the pointer.