Exhaust scavenging is removal of combustion products from the cylinder after the exhaust valve has opened. Obviously this is important so you can get the right amount of charge into the cylinder, with only a controlled amount of exhaust gas left in the cylinder (internal EGR) ready for the next combustion. Too little and you don't get enough fuel/air into the cylinder; too much and you put fuel out through the exhaust.
Opening the exhaust valve at the end of the power stroke is what's known as 'blowdown'. The cylinder pressure at this point is still way above atmospheric, but most of its work has been done. Opening the exhaust valve allows combustion products to begin exiting the cylinder earlier, and at a greater rate, to empty the cylinder more effectively.