Narrowing of the blood vessels due to contraction of their muscles is called vasoconstriction. It slows or blocks the blood flow.
Injury to the blood vessel can cause vasoconstriction. It may also result from medications, disease, etc. Vasoconstriction due to injury allows less blood to be lost. It can also help retain body heat, increase blood vessel resistance and regulate blood pressure. Vasoconstriction of the arteries increases blood pressure, and that of veins increases blood returning to the heart, thereby increasing volume of blood pumped out by the heart (cardiac output).
Severe cold, nerve stimulation, hormones, etc. increase concentration of calcium within the muscles of blood vessel and trigger vasoconstriction. Vasoconstrictors are medications that cause the blood vessels to constrict by contracting their smooth muscles