The vast majority of trans fats in our food are manufactured by adding hydrogen bonds to unsaturated fats. This makes the fat more stable, so it doesn't spoil as quickly. These fats are usually referred to as "hydrogenated fats" or "partially hydrogenated fats". "Fully hydrogenated fats" should not contain significant amounts of trans fats. The evidence is reasonably clear that this type of fat contributes to heart disease.
The other type of fat that has a trans configuration occurs naturally in the milk and meat from certain animals (ruminants, like cows and bison, especially those who have eaten grass as opposed to grain). This type of fat is called conjugated linoleic acid (CLA), and it appears to be good for us - there is a little evidence that CLA can protect from cancer, for example. However, like many naturally-occurring substances, studies on CLA in the form of a food supplement have been disappointing so far.
In summary, it probably isn't the fact that a fat has a trans configuration in and of itself that is the problem. Rather, hydrogenated fats, which happen to have a trans configuration, have a negative impact on health. "Trans fats" has become a shorthand for this type.
Source:
Dietary Reference Intakes for Energy, Carbohydrate, Fiber, Fat, Fatty Acids, Cholesterol, Protein, and Amino Acids (Macronutrients) (2005), Institute of Medicine, Food and Nutrition Board, National Academy of Sciences.
