Double circuit circulation means flowing of blood through heart twice.

in fishes and some other animals the blood enters heart only once

but in human beings,frogs and others the deoxygenated blood flows into the heart and to lungs and again to heart. so it is double circuit circulation and the heart is called double circuit heart.
The right side of the heart receives and pumps deoxygenated blood and left side of the heart receives and pumps oxygenated blood. This circulation is called double circulation.
*The blood is pumped by the right ventricle and it enters the pulmonary artery whereas the left ventricle pumps blood into the aorta.The deoxygenated blood pumped into the pulmonary artery is passed onto the lungs from where the oxygenated blood is carried by the pulmonary veins into the left atrium.This is called pulmonary pathway
*The oxygenated blood entering the aorta is carried by the network of arteries, arterioles and capillaries to the tissues from where the deoxygenated blood is collected by a system of venules, veins and vena cava and passed into the right atrium. This is the systemic circulation.