How do the artery and the vein keep the blood flowing in one direction only?

The heart has valves in the aorta which prevent back flow from the arteries into the heart.

The arteries have some elasticity and can expand slightly when blood is pumped through them at high pressure, the arteries can then contract slightly to maintain the high pressure until the next heart beat. The combination of this and the valves in the heart prevent back flow.

In the veins there are several methods, the valves simply prevent back flow by closing in between heart beats.

Skeletal muscle contracts to prevent blood pooling (build up of blood in veins with closed valves)

And smooth muscle also contracts to help force blood back to the heart.

You are right, heart has valves.

heart pumps the pure blood to the whole part of the body to circulate and in arteries the pressure is maintained so that there in no backward flow of blood and the other reason is the blood in the arteries does not move against the force of gravity.

In veins the deoxygenated( impure) blood is collected and the blood moves against the force of gravity and there is no great pressure in the veins because heart does not pump it so the valves are present to prevent the back flow of blood.

The Heart pumps the blood in one direction ,the blood vessels just channel it ,veins TO the Heart ,Arteries AWAY from it and capillaries are blood vessels for the most part just under the skin .

Because the atria pumps blood into arteries they pretty much go in one direction. In veins however there are one-way values which prevents backwards flow (so it can only move towards the vena cavas)