Because the field of BMI is still young, you will find various definitions from a number of available resources. The definition published by the American Medical Informatics Association (AMIA) is available on their website.
Our local, UNM definition: Biomedical Informatics (BMI) is the science of managing information for health care, research, education and administration by applying, integrating and evaluating information technology along with its associated policies, procedures and organizational cultures. As an interdisciplinary science, BMI extends across the domains of other sciences, which creates sub-specialty fields as outlined in "Video 1 - What is Biomedical Informatics?"
Video 1 - An Introduction to Biomedical Informatics, by Philip Kroth, MD
Video 2 - Big Data Analytics in Health Care, by Michael Bernauer, PharmD
Video 3 - Careers in Biomedical Informatics, by Robby Atala, MD