With respect to environmental law, primacy refers to the rights and responsibilities of the states to oversee day-to-day activities associated with Federal statutes (e.g., the Clean Water Act, SMCRA).
For example, the Environmental Protection Agency (EPA) has ceded primacy to states agencies of Environmental Quality/Protection (e.g., VA DEQ) in order to allow the states to oversee environmental permitting and regulation within their borders. While the states can interpret the Federal laws, review and approve permits, and conduct compliance and enforcement activities, the EPA retains ultimate authority.