Natural heritage refers to the sum total of the elements of biodiversity, including flora and fauna ,ecosystems and geological structures.
Heritage is that which is inherited from past generations, maintained in the present, and bestowed to future generations. The term "natural heritage", derived from "natural inheritance", pre-dates the term "biodiversity." It is a less scientific term and more easily comprehended in some ways by the wider audience interested in conservation.
The term was used in this context in the United States when Jimmy Carter set up the Georgia Heritage Trust  while he was governor of Georgia; Carter's trust dealt with both natural and cultural heritage. It would appear that Carter picked the term up from Lyndon Johnson, who used it in a 1966 Message to Congress. (He may have gotten the term from his wife Lady Bird Johnson who was personally interested in conservation.) President Johnson signed the Wilderness Act of 1964.
The term "Natural Heritage" was picked up by the Science Division of The Nature Conservancy (TNC) when, under Robert E. Jenkins, Jr., it launched in 1974 what ultimately became the network of state natural heritage programs -- one in each state, all using the same methodology and all supported permanently by state governments because they scientifically document conservation priorities and facilitate science-based environmental reviews. When this network was extended outside the United States, the term "Conservation Data Center (or Centre)" was suggested by Guillermo Mann and came to be preferred for programs outside the US . Despite the name difference, these programs, too, use the same core methodology as the 50 state natural heritage programs. In 1994 The network of natural heritage programs formed a membership association to work together on projects of common interest: the Association for Biodiversity Information (ABI). In 1999, Through an agreement with The Nature Conservancy, ABI expanded and assumed responsibility for the scientific databases, information, and tools developed by TNC in support of the network of natural heritage programs. In 2001, ABI changed its name to NatureServe. NatureServe continues to serve as the hub of the NatureServe Network, a collaboration of 86 governmental and non-governmental programs including natural heritage programs and conservation data centers located in the United States, Canada, and Latin America.