First, a primer on baby hearts.
When a fetus is developing in the womb, the lungs are filled with fluid and take up a greater than normal amount of space in the chest cavity. Normally this would prevent the right ventricle from being able to pass blood to the aorta and vice versa, but evolution has gifted us with the ductus arteriosus (DA), which is just a piece of smooth muscle that protects the ventricle from being crushed by the lungs while its pumping. Once we're born our lungs release bradykinin (an amino acid that acts with minor toxicity) which subsequently constricts and kills off the ductus arteriosus.
So back to patent ductus arteriosus (PDA). After a baby's been born, if the lungs do not receive enough oxygen to pump hard enough to release enough bradykinin to close the DA, then the DA remains open and blood pumps irregularly through it. Since this bypasses the rest of the circulatory system and returns to the lungs faster, it essentially creates a traffic jam of deoxygenated blood in the infant's lungs. This causes its body to work overtime to meet its lungs' demands, and this can cause fatigue, shortness of breath, arrythmia, and possibly an enlarged heart.
Generally PDA is treated either by ligation (tying up) of the DA via surgery, or nonsurgically through prostaglandin inhibitors, which force the DA to constrict. The latter is most commonly used in premature babies, who may be suffering from hypoxia or other respiratory problems. Many times, however, patients with PDA show few adverse symptoms and are simply monitored until their lungs grow strong enough to constrict the DA on their own.