Plaques are typically made up of cholesterol and other fats, calcium deposits, cells, and cell debris. They can build up over time, restricting blood flow.
Blood clots can form at the plaque and either obstruct blood flow or break off, affecting the organ connected to the artery. Though more rare, part of the plaque itself can break off and cause an obstruction (embolus).
For example, an embolus from the carotid artery might go to the brain and cause a stroke.

