An aneurysm is an abnormal dilatation of an artery. It can affect any blood vessel but the commonest sites are the abdominal aorta, popliteal artery and the small blood vessels of the brain. The main risks with aneurysms are that the dilated artery has become weakened and therefore it can burst, leading to catastrophic bleeding. Sometimes, blood flow within the dilated blood vessel become turbulent, leading to the blood clotting within the aneurysm. This blood clot can progress to completely block the artery or may break free from the artery and travel to other parts of the body. Depending on the size of the aneurysm, they usually require treatment.
For those who would like more information, see the peripheral aneurysm PDF. There is a lot of medical and surgical terminology in this document.