The answer is very simple really. Trans-fats get a bad name because they are linked to the increased rates of coronary heart disease and many related risk factors.
Coronary heart disease is caused at a basic level by the pipes of the bodies blood transport system, the arteries, veins and capillaries becoming less elastic, and more prone to blockages as a result.
Trans-fats are a certain type of fat with cis-fats being another. The fats are essentially the same with the cis and trans name denoting a type of bond used within the fat. The key difference is that cis bonds lead to flexible structures whereas trans bonds are firmer and stronger.
Thus trans fats are perfect for baking and cooking as they thicken recipes. Unfortunately they have the same effect in the blood system. When too many fats are eaten they 'fall' off their hdl and ldl transport proteins while travelling around the body. The cis fats being flexible carry on round the body. The trans fats being more rigid often get stuck and attach to the walls of veins, arteries and capillaries. Sometimes this is where damage has occurred and the trans-fats get trapped and inhibit the natural healing process.
As a result, these vessels lose their elasticity overtime and become less able to adjust to the pressures and requirements of daily life. the heart has to work much harder because now the same volume of blood is being forced through a system that cannot expand to cope with it. This leads to a corresponding rise in blood pressure. This is a challenge that eventually becomes too great and sooner or later a weakpoint develops.
The weakpoint can be; a) A haemorrhage, where a blood vessel leaks or ruptures, or b) a clot may form and either directly block a vessel or it may break off and travel around the blood network until it reaches a point it can't get through.
Either way this often has a bad effect on the body and can lead to a stroke, heart attack or other sad event.
So in short, trans-fats are a problem because they're rigid and in flexible. This means that in the body they make it difficult for the blood network to function properly. Over long periods they can help create fatal conditions where the blood system is too rigid and inflexible and breaks under high load.