High cholesterol causes deposits of fat, called plaques, to build up in the blood vessels. This can restrict blood flow through the arteries and these deposits can break off to cause a stroke or heart attack. The restricted blood vessels can inhibit the amount of oxygen and nutrients that reach the muscles in the heart, causing chest pain, or angina. High cholesterol raises the risk of developing heart disease and having a stroke. Heart disease is the leading cause of death in the United States, and strokes are the fifth leading cause of death.
Reference:
CDC: https://www.cdc.gov/cholesterol/facts.htm
Mayo Clinic: https://www.mayoclinic.org/diseases-conditions/high-blood-cholesterol/symptoms-causes/syc-20350800
NHLBI: https://www.nhlbi.nih.gov/files/docs/public/heart/chol_tlc.pdf