To "make rounds" is to go from room to room evaluating patients in a hospital. The physicians who are rounding discuss the case, talk to and examine the patient, and discuss with the patient and/or nurse the next steps in the medical plan.

Doctors 'make rounds' when they go around the hospital to each patient and check on them. With computers and other technology doctors can check on their patients remotely, they don't have to be in the same physical place. They can video conference and also the patient can have machines and gadgets at home which check their health (blood pressure, insulin etc etc) and can upload the information for the doctor to review.