In Ascherio & Willen (1997) it is mentioned that, and I quote:
[...] Trans fatty acids increase plasma concentrations of low-density lipoprotein (LDL)
cholesterol and reduce concentrations of high-density lipoprotein (HDL) cholesterol relative to the parent natural fat. [...] [T]rans fatty acids increased the plasma ratio of total to HDL cholesterol nearly twofold compared with saturated fats. On the basis of these metabolic effects and the known relation of blood lipid concentrations to risk of coronary artery disease, we estimate conservatively that 30 000 premature deaths/y in the United States are attributable to consumption of trans fatty acids.
The US Heart Foundation explains in more layman's terms the same principles:
Trans fat is a type of unsaturated fat that behaves like a saturated fat because of its chemical structure. It increases our risk of heart disease by increasing the “bad” LDL cholesterol, while also lowering the “good” HDL cholesterol in our blood.
And from the Better Health Channel Australia we learn why LDL is 'bad':
Too much cholesterol circulating within LDL in our bloodstream leads to fatty deposits developing in the arteries. This causes the vessels to narrow and they can eventually become blocked. This can lead to heart disease and stroke.
Ascherio & Willen, Am J Clin Nutr 1997;66(suppl):1006S-lOS.