Heart valves are the doorways between heart chambers. The doorways open and shut depending on 1 key ingredient: pressure. The heart works somewhat passively and uses pressure gradients and differences in that pressure to its advantage. Everything in nature likes to be in balance it likes to be even. When things are out of balance nature passively restores the balance by way of diffusion. Diffusion states that things air/water/blood moves from a region of higher concentration to an area of lower concentration, from an area of a lot of something to an area of less of something. The cardiac valves simply uses this pressure difference and allows blood to flow in only one direction.
The heart valves are like pressure switches, once an area like the right atrium reaches a certain pressure point it over comes the resistance of the valves and the pressure difference of the right ventricle and blood pours in until the pressure is equal and as soon as the pressure changes in the right ventricle to be more than the right atrium blood starts to move back towards the right atrium, but instead of just flowing back and forth between the two chambers the tricuspid valve slams shut (Lub, the first heart sound) just as the right ventricle starts to contract.
The papillary muscles that attach to the mitral and tricuspid valves help to keep the valves water tight and prevent any leaks. The papillary muscles attach on the ventricle side. The extra muscle is needed to hold the door shut as the right ventricle has enough force to blow open the door to the opposite side. The papiallry muscles hold the door shut against extreme pressures. As the blood pours into the right ventricle the right atrium contracts and forces more blood in the ventricle now the muscles of the right ventricle are charged or stretched and will perform a stronger more efficient contraction. As the right ventricle contracts the papillary muscles use the muscle contraction of the right ventricle as leverage to keep the door shut. If it didn't have these extra tendons holding onto the door, the amount of pressure the heart could generate would force the blood back into the right atrium.
Blood likes to travel the path of least resistance as in all things in life. In this case the pulmonary valves open and since there is more pressure in the right ventricle than in the pulmonary arteries, blood gets squeezed into the artery. As the right ventricle empties the pressure between the pulmonary artery and the right ventricle equalizes the flow of blood stops. As the pressure of the pulmonary artery increases the light pressure is enough to force the pulmonary valve shut and prevent the back flow or regurgitation from entering the right ventricle. The pulmonary valves don't require such extreme measures as the papillary muscles because the pressure in the pulmonary artery is not high enough to break open the door. The gentle back flow is just enough force to close the pulmonary valve and prevent back flow.
The blood proceeds to the lungs where it picks the much needed oxygen to be delivered to the body. Think of the red blood cells as tiny oxygen delivery trucks picking up it's load and heading on down the highway. These trucks are about to encounter the most terrifying part of it's journey; the dreaded left ventricle. The powerful muscle of the left ventricle has enough power to overcome the pressure of the circulatory system. Just think how much force is required to overcome 5 liters of blood in the human body by one muscle half the size of your fist. That is a daunting task to say the least. Your left ventricle has been working out your entire life, it is up for the challenge and then some.
The blood regroups in the left atrium all lining up to enter the left ventricle via the mitral valve. As the pressure builds in the left atrium, the door starts to open again allowing the blood to spill into the left ventricle. Once the pressures equalize blood stops flowing, but the left atrium at that very second gives an extra squeeze and forces the very last drop of blood into the left ventricle to over capacity. This causes the left ventricle to stretch slightly and increases the pressure significantly. At that very moment the mitral valve slams shut and the left ventricle unleashes it's fury on the tiny trucks, making the oxygen delivery.
The intense pressure is so great it has enough force to overcome pressure of the entire body. Let's assume your blood pressure is 120/80. This resting pressure in the aorta is the bottom blood pressure reading the doctor takes on your arm (80). The pressure the left ventricle exerts is the top part of the blood pressure reading (120). So by knowing these 2 readings we have a good idea on the shape of your overall health. The larger the bottom number the more pressure your heart has to generate to overcome that pressure. That in turn causes more work on the heart and could lead to potential life threatening conditions; CHF, hypertension and stroke to name a few.
The blood fires from the left ventricle through the door of the aorta called the aortic valve. Again as the pressure equalizes and then the blood pressure of the aorta overcomes the pressure of the left ventricle the aortic valve slams shut (Dub, the second heart sound) and the process starts all over again as it returns back to the right atrium, eventually.