How can a diet high in fats lead to heart disease?

A diet high in fat can lead to the formation of atheroma plaques with in blood vessels. These plaques make the walls of vessels rougher which increases the likelyhood of a clot forming. If a clot moves to, or forms in, a vessel supplying blood to cardiac muscle it may block blood flow. This means that stops the muscle from getting oxygen and so it starts to die. This is a myocardial infarction or heart attack. The plaques also weaken the walls of blood vessels making aneurisms more likely.