Why do people say that trans fatty acids are bad for your health?
Trans fatty acids are digestible, but they cause an increase in LDL and a decrease in HDL, which is the leading mechanism for atherosclerosis. So, they increase the risk of a cardiac infarct. 

LDL means Low Density Lipoprotein, it's one of the 5 major lipoprotein groups. Lipoproteins carries the fatty acids and cholesterol which were absorbed from intestines (because lipids are hydrophobic and cannot be carried within the blood directly like glucose or proteins.) 

So, LDL mainly carries cholesterol and fatty acids from intestines to tissues. (fatty acids and cholesterol are essential for cells.) But in excess levels, they tend to accumulate in vessel walls, which also starts and inflammatory response and makes the situation worse. (mainly includes macrophages and T cells) This is the main mechanism for atherosclerosis. 

In the other hand, HDLs serve as a reverse cholesterol transport system, which carries the cholesterol back, mostly to the liver (for bile secretion) or steroidogenic organs such as adrenals, ovary, and testes by direct and indirect pathways. So a high HDL reduces the atherosclerotic process.