Why do high cholesterol levels result in a buildup of fat in blood vessels?
The phrase "high cholesterol", and the measurement itself is a marker for high levels of a particular lipoprotein, Low density lipoprotein (LDL). Because cholesterol and triglycerides are not soluble in plasma, they are packaged by the liver into soluble particles called lipoproteins. Packaged in lipoproteins, these lipids are transported throughout the body, for use by different organs and tissues. As these lipids are dropped off, the lipoprotein is converted from one form to another, with characteristic biophysical and physiologic properties. The LDL is a late stage of a lipoprotein before reuptake at the liver (and other organs, but mainly the liver) via the LDL receptor. We happen to know that people who have high levels of circulating LDL are at risk for, e.g., cardiovascular disease because of The Framingham Study, and that if you can reduce circulating LDL levels you can decrease the risk for these diseases. The molecular basis of this risk was demonstrated to be, in large part, failure of clearance of LDL particles because of ineffective receptor mediated endocytosis, as described in this wonderful 1986 paper in Science.

From this presentation:


Some LDL cholesterol circulating through the bloodstream tends to deposit in the walls of arteries. This process starts as early as childhood or adolescence.
White blood cells swallow and try to digest the LDL, possibly in to digest the LDL, possibly in an attempt to protect the blood vessels.
In the process, the white blood cells convert the LDL to a toxic (oxidized) form.
More white blood cells and other cells migrate to the area, creating steady low steady low-grade inflammation in the artery wall.
Over time, more LDL cholesterol and cells collect in the area. The ongoing process creates a bump in the artery wall called a plaque. The plaque is made of cholesterol, cells, and debris.
The process tends to continue, growing the plaque and slowly blocking the artery.


There is a good overview of the general physiology here in Robbins The Pathologic Basis of Disease. Chapter 5, Genetic Disorders, reviews the physiology, and the relevance to disease, in the section on Familial Hypercholesterolemia. The review is relevant to hypercholesterolemia in general.