There are lots of possible definitions. Here's my current favorite:

Biomedical Informatics is the science underlying the acquisition, maintenance, retrieval, and application of biomedical knowledge and information to improve patient care, medical education, and health sciences research.

Since it is a science, it should not be confused simply with applying information technology to the medical domain.
(credit to Charles Friedman for a similar definition)

I would also add that a primary feature of Biomedical and Health Informatics is its interdisciplinary nature: It connects computer science, medicine, biology and health care, and provides a synergy that goes beyond anything that researchers in any single domain can provide.

Here is material copied from the AMIA web page:

Medical informatics has to do with all aspects of understanding and promoting the effective organization, analysis, management, and use of information in health care. While the field of medical informatics shares the general scope of these interests with some other health care specialties and disciplines, medical informatics has developed its own areas of emphasis and approaches that have set it apart from other disciplines and specialties. For one, a common thread through medical informatics has been the emphasis on technology as an integral tool to help organize, analyze, manage, and use information. In addition, as professionals involved at the intersection of information and technology and health care, those in medical informatics have historically tended to be engaged in the research, development, and evaluation side, and in studying and teaching the theoretical and methodological underpinnings of data applications in health care.

See also the AMIA FAQ for more.

John Gennari: updated on July 22, 2002