What is it?

According to Wikipedia, biomedical engineering is:

"the application of engineering principles and techniques to the medical field. It combines the design and problem solving expertise of engineering with the medical expertise of physicians to help improve patient health care and the quality of life of healthy individuals." (remember this last part here; it's important!)

And this is applied how?

Besides clinical devices, such as MRI scans, biomedical engineering is also responsible for numerous medical devices. Hip replacements, artifical hearts, pacemakers, and even dentures. Beyond the now generally common, new advances in the field have lead to neural prosthics...