Final answer:
The public health core function being utilized when a nurse provides essential health services to underserved individuals is 'assurance'. This function ensures the availability and effectiveness of necessary health services in the community.
Step-by-step explanation:
When a nurse ensures that individuals who would not normally have access to health care are provided with essential personal health services, they are engaging in the public health core function of assurance. Assurance refers to the role of public health organizations to ensure that services necessary to achieve agreed upon public health goals are available and effective. This can include enforcing laws and regulations that protect health and ensuring access to care. Other core functions include assessment, which is systematically collecting data on the population, analyzing it, and making it available to where it is needed; and policy development, which is the process by which society makes decisions about problems, chooses goals and strategies to address the problems, and allocates resources to reach them.