Cholesterol deposits on the inner wall of the vessels,
particularly at bifurcation site, then
ulcerations occur on these cholesterol deposits

At later stages, platelet aggregants form on top of the
ulcerated site of the cholesterol deposits, enlarging in size and causing
stenosis of the vessel lumen

When the platelet aggregant grow in size, it becomes fragile
and easily can brake and dislodge distally in the vessel causing obstruction
in smaller branches. Also if the stenosis increases progressively, it
eventually might cause complete obstruction of the vessel.
See this dynamic
image illustration