Because, like most arteries, the aorta is under tremendous pressure, it is a very thick vessel to resist pressure and prevent leakage. Unlike the other arteries, the aorta actually uses a double wall structure, essentially making the blood carrying part a tube within a tube. However, the two tubes are not fused together in any way.
In most people, there is a seal at the ostium to prevent blood leaking into the space between the two aortic tubes. However, in very rare cases, blood will start leaking into the space between the two tubes. As the outer aortic wall is perfectly capable of holding in this blood, but it has no where to go, and the blood is under pressure, blood eventually fills up the space, compressing the inner tube and preventing blood from passing through it. If untreated, the aorta becomes blocked and the patient dies of oxygen deprivation.
Aortic dissections are very hard to diagnose. They are rare and the symptoms they present almost exactly match that of a heart attack (even though the coronary arteries will still be getting blood). The only way to definitively diagnose a dissection is with a CT Scan. After that, the patient needs to be put on bypass until their aorta is surgically repaired.
If caught in time, the prognosis is generally very good. However, patients generally only have a few hours between the time symptoms present and death.
One of the best known victims of an aortic dissection was actor John Ritter.