What is minimally invasive heart bypass surgery?

It depends. Minimally invasive surgery can mean many things. The majority of cardiac bypass surgery is done using the heart lung machine and stopping the heart (on pump). But some surgeons do it with the heart beating (off pump). Other surgeons do it thru a 3-4 in incision between the ribs. Others do it thru several 1 inch incisions with the robot. These also can be done on or off pump.
Smaller incisions. Instead of opening the chest widely, the heart is accessed through smaller incisions. This may result in a shorter recovery. Of course, having restricted access to the heart limits the areas that can be treated, thus this procedure may not be possible in many cases.