The heart is actually two pumps that work in parallel to push blood through the lungs where it acquires oxygen which is then pushed around the rest of your body to provide oxygen and nutrients to all your vital organs.
Structure
Each pump consists of two chambers called the atria, which collects the blood, and ventricles which either push the blood through your lungs or around your body. The two chambers are separated by a valve to prevent blood being sent in the wrong direction.
There are also valves at the origin of the main blood vessels leaving your heart to prevent blood re-entering your heart once it has been ejected.
Diseases that affect the valves can lead to strain on the various chambers and ultimately result in a reduction in the ability for the heart to function effectively.
Circulation
The heart muscle has its own blood vessels called coronary arteries which provide food and oxygen to keep it healthy and functioning.
If these arteries become narrowed, then the heart muscle may not get enough oxygen leading to angina which may present as exertional chest pain.
If the arteries block completely, then this will cause a heart attack or myocardial infarction resulting in potentially permanent damage to the heart muscle.
Electrical function
In order for the heart to keep beating, it also has its own electrical system which is not only able to spontaneously generate an electrical signal every time your heart beats but allows the signals to spread evenly across your heart so that it beats synchronously.
As the electrical signals pass through the heart, it causes the heart muscle to contract, and you have a heartbeat.
Diseases of the electrical system can cause slow heart rates (bradycardia) or fast heart rates (tachycardia). Although most fast heart rates are not dangerous, very rarely they can result in cardiac arrest when the heart stops pumping completely.
If the heart muscle is damaged or cannot generate enough force, then it may not be able to pump blood around the body properly resulting in heart failure.